For $R > 0$, assume ΓR is a circle $\{z \in \mathbb C : |z| = R\}$ with anticlockwise direction. For which $R>0$, is $f(z) = \int\limits_{ΓR} \frac{1}{\sin^2(z)} dz$ continous on ΓR and evaluate the integral over this ΓR.
As sin is continuous everywhere I found that I am just required to find the contour integral over 0 to infinity ie
$\int\limits_0^\infty \frac{1}{\sin^2(z)} dz$.
I am given the information that $\sin(z) = \frac{e^{iz} - e^{iz}}{2i}$ but confused on how to find it for $\sin^2 (x)$ as asked in the question.