And like every single Japanese manga, because Vina walked in the rain, it automatically means that he's going to get a cold. Oh, but wait, the solution is simple. By the next afternoon or evening at latest, he'll be perfectly fine.
Honestly, I kind of want Takane to not have romantic interest in him. First, harems are usually crap. Second, it's a nice dynamic to have her as just a friend who feels some kind of connection with him. It doesn't have to develop into romance to be good.