Find Line integral of $e^{-z} /{z-\pi/2}$ on a region $\gamma$

Question

Let $\gamma$ be the diamond connecting points $x=2, -2$ and $y=2, -2$. and its oriented positively (counter-clockwise, I believe?). I'm not so sure if we can use the Cauchy integral formula here and just say that our answer is $2\pi i e^{-\pi i/2}$.