Answer
The function $\csc x^2$ is discontinuous at $$ x=\pm \sqrt {n \pi}$$
and the discontinuity is infinite.
Work Step by Step
Since $\csc x^2=\frac{1 }{\sin x^2}$, then the function is discontinuous when
$$\sin x^2=0.$$
That is, $ x^2=n\pi $, n is an integer. This means that the function $\csc x^2$ is discontinuous at $$ x=\pm \sqrt {n \pi}$$
and the discontinuity is infinite.
