That is, how can one solve the equation
$\cos(\pi t)\sin(t) = \cos[\pi(t+T)]\sin[t+T]\text{ for all } t\in\mathbb{R}^+$
for $T$ assuming that $T$ is also a positive real? I have tried using a whole load of trig identities and tricks but frankly, it's just a mess and I don't want to regurgitate that nasty stuff here. Upon plotting the function I can see that $T\approx 50$ (that it indeed has regular periodicity on a seemingly large-ish interval) but I have no idea how to determine this analytically. Any help is appreciated.