#### Answer

Fill the blank with
... $(1, \displaystyle \frac{\pi}{4})$ ...

#### Work Step by Step

Inverse functions have graphs that are reflections of each other relative to the line y=x. This means if (a,b) is on the graph of one, then (b,a) is on the graph of the other.
To make $\tan x$ a one-to-one function, we restricted
its domain to $(-\displaystyle \frac{\pi}{2},\ \displaystyle \frac{\pi}{2})$ and $\displaystyle \frac{\pi}{4}\in(-\frac{\pi}{2},\ \displaystyle \frac{\pi}{2})$, so
$\displaystyle \frac{\pi}{4} $will be in the range of its inverse.