My task is to find
$$\int_{|z|=6}tan(z)dz$$
So i was trying to find it using residue theorem.
I found that
$$Res(f(z),\frac{\pi}2+\pi n)= \frac{sinz}{-sinz}=-1$$
Now by the residue theorem
$$\int_{|z|=6}tan(z)dz=2\pi i\sum_{k=0}^nRes(f(z),z_n)$$
My question is how do i calculate this?
I have an infinite singular points.
Do I just set the $-1$ in the sum? Won't i get an infinite residue, is it possible?