Find $\csc 330^\circ.$
We have that
\[\csc 330^\circ = \frac{1}{\sin 330^\circ}.\]Since the sine function has period $360^\circ,$
\[\sin 330^\circ = \sin (330^\circ - 360^\circ) = \sin (-30^\circ) = -\sin 30^\circ = -\frac{1}{2},\]so
\[\frac{1}{\sin 330^\circ} = \boxed{-2}.\]