$tan(x)$ isn't defined for values $x=n\pi+\pi/2$ where n is an integer.
Work Step by Step
To understand where tan(x) isn't defined let us understand the function definition. tan(x) is defined as the sine of x over the cosine of x. So when ever $cos(x)$ isn't defined, we have ourselves an undefined value. $cos x=0$ at the values shown on the unit circle AND all added rotations.