Residue calculus

[Guest]

I would like to ask if somebody know how to calculate the integral:
$\int_{|z|=\frac{2}{n}}\frac{z+1}{\sin(n^2z^2)} \ dz$.

It is my homework and I would like to dig out of it. We should use a book Complex Analysis
Authors: GAMELIN, THEODORE a chapter 7 residue calculus. But I don't know how to connect a theorem which is described there with these example. Please could you help me. Maybe if you know some other literature or you know how to calculate it. Maybe it is easy, but I totally don't know how to start.
Thank you.