Calculus and Trigonometry?

It seems to me you should be able to relate the sides with the law of sines, or the law of cosines.

Then dθ/dt = Sin(ωt) gives θ(t) = -Cos(ωt)

This is a related rates problem, but make sure you make sure there isn't a conflict between the argument of these trig terms, specifically the "ω" parameter, and dθ/dt, since ω = dθ/dt

You might want to see if you can use vectors to relate the sides. It may be less messy, but your goal will be to get an equation for the missing side as a function of θ I would think, then as θ changes the length of that side changes as well.

Take the derivative and at that point you should be able to identify the key components from the information in the question and solve for dL/dt (the rate of change of that side, which I called "L" with time). Then you can substitute for t, which you said is: t = π

Yes

Si