Trouble calculating residues

Hello,

I'ld like to calculate the reside of $\displaystyle f(z):=\frac{z^{n-1}}{\sin^n(z)}$ at $\displaystyle z_0=0$.

Using the definition I get $\displaystyle \text{res}_{0}f = \frac{1}{2\pi i} \int_\kappa \frac{z^{n-1}}{\sin^n(z)} dz$, but I cant compute this integral.

My next idea was to develop the function into a Laurent-Series and use the coefficent $\displaystyle a_{-1}$ but thats basically the same calculation.

I would like to get some help on how to solve this and similar problems.

Thank you!