Answer
$\displaystyle \frac{\pi}{4}$
Work Step by Step
$y=\tan^{-1} x$
Domain: $(-\infty, \infty) $
Range: $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$
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$y$ is the number from $(-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2})$ such that $\tan y=1$
$\displaystyle \tan\frac{\pi}{4}=1\qquad$and$\displaystyle \quad \frac{\pi}{4}\in(-\frac{\pi}{2}, \displaystyle \frac{\pi}{2})$
so
$\tan^{-1} 1 =\displaystyle \frac{\pi}{4}$