Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.3 One-sided Limits; Continuous Functions - 14.3 Assess Your Understanding - Page 891: 68

all real numbers apart from $n\pi$, where $n$ is an integer.

We know that the cosecant function undefined for $n\pi$, where $n$ is an integer, hence it is continuous everywhere, apart from where it is undefined, therefore it is continuous for all real numbers apart from $n\pi$, where $n$ is an integer.