Answer
$\left\{x\in\mathbb{R}|x\ne\frac{\pi}{4}+n\pi, x\ne\frac{\pi}{2}+n\pi,n \text{ is an integer}\right\}$.
Work Step by Step
The function is defined for all real x where the denominator
$1-\tan x\ne0$.
When $1-\tan x=0$,
$\tan x=1$
$x=\frac{\pi}{4}+n\pi$ (n is an integer)
The function is also undefined when
$x=\frac{\pi}{2}+n\pi$
as $\tan x$ is undefined.
$\therefore$ the domain is all real $x$, exluding $x=\frac{\pi}{4}+n\pi$ (n is an integer) and $x\ne\frac{\pi}{2}+n\pi$ (n is an integer).
