This is from a practice exam that we are working on, problem number 2. We were thinking first to use Cauchy-Goursat, but then the problem only says that the curve doesn't lie on the singularities of $\sin^2(z)$. They might still be interior to the curve. Is there another way to approach the problem using theorems we might know?
Edit: The question is : Prove that $\int_C\frac{\cos(z)\mathrm dz}{\sin^2(z)}=0$ where C is any simple closed contour not passing through a zero of $\sin(z)$.
Edit: I don't know about residues.