Complex Analysis – Determine the Singularity at Infinity

Question

I'm wondering why the function
$$
\frac{z(z^2-\pi^2)}{\sin(z)}
$$
has a nonisolated singularity at infinity? I can identify the singularities which are removable or simple poles here, but sometimes I'm confused with how to discuss the case at infinity.

Thanks for the help!

Answer 1

No, $\infty$ is not an isolated singularity, since every natural number greater than $1$ is a singularity too.