Answer
$-\frac{\pi}{4}.$
Work Step by Step
The domain of $\tan^{-1}{x}$ is the range of $\tan{x}$, which is the real numbers.
The range of $\tan^{-1}{x}$ is a specified domain of $\tan{x}$, i.e. $\left(− \frac{\pi}{2} , \frac{\pi}{2} \right)$.
We know that if $\tan y=x$, then $\tan^{-1}(x)=y.$
We know that $\tan(-\frac{\pi}{4})=-1$, hence $\tan^{-1}(-1)=-\frac{\pi}{4}.$