# Laurent series expansion of functions $\frac{1}{z\sin z}$ and $\frac{e^z}{z(1-e^{-z})}$.

I know there are several questions about Laurent series expansion by here. But I really couldn't find the expansion of

$$f(z)=\frac{1}{z\sin z} \ \ \ \mbox{and} \ \ \ g(z)=\frac{e^z}{z(1-e^{-z})}$$

around $z=0$ using the related answers. I'm able to deal only with rational functions or functions with $\sin$, $\cos$, $\log$ in the numerator. Then I'd like to ask some hint. Thanks in advance!