Hey guys, quick question. How would I go about showing that this following equation:

$\displaystyle \int_{|z|=3}^{}tan(z).dz$

equals $\displaystyle -4\Pi i$

...I've tried breaking it down to $\displaystyle sin(z) / cos(z)$, then finding the residues using the singularities that occur at $\displaystyle \Pi /2$ and $\displaystyle -\Pi /2$ but that just leads me to an answer of 0.

If anyone could show me how to do this using the residue theorem, I'd really appreciate it. Thanks.