I can see Togami doing a half-assed job of framing Syo and thinking "Ah, those idiots will never know the difference." It's stupid, but in an overwhelmingly arrogant way.
I suppose I can see him finding a body and jumping to the conclusion Syo did it, though I'm not entirely comfortable with that one, since everybody in the crowd has the potential to be a murderer. In fact, we just had a murder which had nothing to do with Syo. You'd think he'd want something more than a hunch, but again, he's awfully arrogant and perhaps not all that smart. Maybe he never considered that his hunch could be wrong.
I can't see him framing the scene to try to force Syo into the open. It would seem to do the reverse. Admitting you're a serial killer is never going to make you popular, but doing it when there's a dead body with your MO would be near suicide.
I'm stuck for why he'd go into the girl's workout room. Unless it had something to do with bicycle seats and his dark secret....
Perhaps Syo told him she was going to kill, just to mess with his head, and happened to do it the night there really was a murder?
...You mean... like he just tried to do...? And Syo and Naegi JUST proved him wrong about...?
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Xbox GT: PrivateBiscuit1
Down with Zhang. Let there be Biscuit!