Doesnt he realize he can just explain the situation and why he needs the 3 sizes? I mean, thats how most of these conflicts can be solved and are solved
If these guys could communicate properly, the drama woulda ended by chapter 10.
And it probably wouldn't have gone the way it was meant to, either, in that case. Part of the core of this story is the fact that Kosaki and Raku can't tell each other how they feel so Raku and Chitoge can develop legitimate feelings for each other through the 'false love' relationship and, I suspect, end up together once the love turns real. We already have Chitoge admitting to herself that she loves him, finally, so now it's Raku's turn to realize he actually likes Chitoge, and then might even like her more than Kosaki.
Anyway, the whole premise for this chapter was pretty absurd, and Chitoge even lampshades it by thinking to herself that she believed him. I mean, it's her gang that dropped the case off. Why wouldn't she cooperate if he prefaces asking her with the fact Beehive guys gave it over to him?
But yeah, it's only to be expected for the sake of comedy that he'd take the riskiest and stupidest path to trying to figure it out, fail miserably in the end, and be forced to just ask straight out anyway, but in the stupidest, most publicly shaming way possible. Only for it to end up not being her three sizes, but that narcissistic Claude's.
To be honest, I'm glad this one didn't get adapted into the anime's second season. It's a very weak chapter that feels like it ruins the efforts to protect Raku from being exposed and labeled a pervert in the hot springs back during the school trip. What was the point of all that effort if he's just going to get branded like this here?