Ok, I sat here and really tried to come up with something that makes at least a little sense. I've tried to split it up into multiple easy to read paragraphs because I'm long-winded. Here's my theory as to what's going on.
Shizuku has some sort of heart problem and probably needs a heart transplant. Only she and her mother know about this. Even in a country with universal healthcare, the odds of her getting a heart and paying for the procedure are slim to none. Shizuku's mom approaches Takt's father the politician (or perhaps uses sources of her own) to find some wealthy benefactor that can help them out. In turn, Shizuku is promised to the benefactor as a wife/plaything/mistress/whatever. Shizuku and her mom are not happy about this but it's somewhat better than Shizuku dying.
It would be juicy if said benefactor is Takt's father and that Shizuku is promised to Takt's father or perhaps one of Takt's brothers. Shizuku and her mother decide not to say anything about Shizuku's health or any deal(s) made to Takt or Riku. Also, Takt would not be privy to this information even if his father is the one making the deal because as shown in chapter 66, Takt's family hates him for some reason (might stem from him potentially being gay but it's not specified yet).
Shizuku knows she's living on borrowed time. She has to transfer schools (perhaps just an excuse and she's really going to a hospital for the transplant and will then become someone else's property). She's been in love with Riku for a long time but neither she nor he has had the courage to really do anything about it. Enter Takt. For whatever reason (either Takt is gay and in love with Riku or he's just super possessive of Riku) Takt asks Shizuku to date him. The speculation is he wants her away from Riku (again for whatever reason) just like he originally dated Umimi for the same reason.
At this point in time, Shizuku is not aware of Takt's true feelings. She has limited time and wants the rest of what time she has left to be with her friends and full of happy feelings. I guess she assumes that if she rejects Takt here it might drive a wedge between the three of them and ruin the few months she has left. This is where she makes a deal with Takt. She mentions the deal in chapter 64 where she enjoyed the time the three of them spent together like real friends. While the deal isn't explicitly mentioned verbatim it appears that it's something like Takt must go no further than making out and the two of them need to act normal in front of Riku and act like everything is ok and they're all friends. The deal lasts from the moment they start dating to the moment Shizuku transfers out of their school. If Takt keeps his end of the bargain, then Shizuku promised him that for whatever time she has left she belongs to Takt.
We know she's a virgin as she told Riku that and in chapter 64 Takt asks her to continue "from where we left off that day" which I believe is referencing one of the early chapters where Shizuku is taking a bath and a hickey is visible on her neck. So it seems obvious that Shizuku and Takt were kissing/making out at the very least as Shizuku has had hickeys in the past and the relative ease with which she French kisses Takt in Chapter 64 and 65.
So, Shizuku's main goal now is to keep things friendly, keep her health and transfer a secret from both Riku and Takt and convince Riku to take her virginity so she can at least lose it to the man she loves. She doesn't want to tell Riku the truth as she feels it will hurt him less if she just disappears from his life rather than tell him she's having to sell herself to someone to save her life.
Riku consistently fails to take her up on her offer and time runs out so she's forced to honor her end of the deal with Takt. However, she's unable to keep her feelings to herself as Takt undresses her and mentions that she's in love with Riku which prompts Takt to be all "I've always known."
Here's where I'm a bit iffy as Takt seems more than willing to make out and have sex with Shizuku. If he's gay, is he forcing himself to be heterosexual to please his family? Is he bisexual instead of gay? Is he gay but he's doing it to corrupt Shizuku in the hopes that Riku won't want her anymore?
At one point in Chapter 65 Takt gets her fully naked and is reaching for her vagina while saying "Don't worry, I'll have you giving in right away---". That doesn't sound like something he'd say if he was gay but again maybe this is all a mask for him. I'm thinking it is a mask because right after Shizuku apologizes to him which causes him to yell "This isn't right!! Get mad at me! Say I'm awful!" Takt knows what he's doing isn't right. He's also started to or has been crying which is revealed shortly after. It's obvious he's somewhat conflicted and then we get into Shizuku mentioning she noticed he's been hurting for a long time and she thinks it's because he's always loved (Riku) but doesn't get to finish as Takt screams and runs away.
We're then given a scene of Shizuku naked and on the ground lamenting "I wonder where did I go wrong..." I dunno, lady, maybe when you decided to take all agency away from the guy you love and lie to everyone and make weird ass deals instead of telling the truth. But I don't blame the characters for the way the author chooses to write them.
