Answer
$x=-2\pi,-\pi,0,\pi,2\pi$, $\csc{x}=\frac{1}{\sin{x}}$
Work Step by Step
If $x=-2\pi,-\pi,0,\pi,2\pi$, $\csc{x}=\frac{1}{\sin{x}}$ has vertical asymptotes because $\sin{x}=0$ at those values, hence the denominator is $0$, therefore $\csc{x}$ is undefined at those values. (see graph)