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: 67

all real numbers apart from $\frac{(2n+1)}{2}\pi$, where $n$ is an integer.

We know that the tangent function undefined for $\frac{(2n+1)}{2}\pi$, 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 $\frac{(2n+1)}{2}\pi$, where $n$ is an integer.