Find the principle part of the Laurent expansion of the function $f(z) = \frac{1}{(e^z - 1)^2}$ about $z = 0$. Hint: First show that $f$ has a pole of order $2$ at $z = 0$.
I already found the pole of order $2$ using Laurent expansion. But I am not able to proceed further with finding the principle part.
Thank you