Determine and classify all singular points
Determine and find residues for all singular points $z\in \mathbb{C}$ for
(i) $\frac{1}{z\sin(2z)}$
(ii) $\frac{1}{1-e^{-z}}$
Note: I have worked out (i), but (ii) seems still not easy.
Related problems: (I), (II), (III). Just use the following test, a function $f(z)$ has a pole of order $m \in \mathbb{N} $ if
$$ \lim_{z\to z_0}(z-z_0)^m f(z) = c \neq 0, $$
where c is a finite number. For instance, in your case, $z=0$ is a pole of order $2$, since
$$ \lim_{z\to z_0}z^2 \frac{1}{z\sin(2z)} = \frac{1}{2}.$$
For finding residues see here.