Chapter 6 - Trigonometric Functions - 6.3 Properties of the Trigonometric Functions - 6.3 Assess Your Understanding - Page 395: 100

$\theta=k\pi$, where k is an integer

Since $\csc(\theta)=\frac{1}{\sin\theta}$, then it is undefined when the denominator (which is $\sin{\theta}$) is $0$. Recall that $\sin\theta=0$ if $\theta=k\pi$, where $k$ is an integer. Therefore, the function is undefined when $\theta=k\pi$, where k is an integer.