Where is $ f(z) = \tan z$ nonconformal?

Question

I need to determine where the complex mapping $f(z) = \text{tan}z$ is nonconformal.

The answer is that $f(z)$ is nonconformal at the points $z = \frac{(2n+1)\pi}{2}$, $n=0, \pm 1, \pm 2, ...$ but I'm not sure how figure that out.

Thanks