Answer
$$ - \frac{\pi }{4}$$
Work Step by Step
$$\eqalign{
& {\tan ^{ - 1}}\left( {\tan \left( {3\pi /4} \right)} \right) \cr
& {\text{We first calculate tan}}\left( {\frac{{3\pi }}{4}} \right),{\text{ }}\theta = \frac{{3\pi }}{4}{\text{ is in the quadrant II}}{\text{, then}} \cr
& {\text{tan}}\left( {\frac{{3\pi }}{4}} \right) = - 1 \cr
& {\tan ^{ - 1}}\left( {\tan \left( {3\pi /4} \right)} \right) = {\tan ^{ - 1}}\left( { - 1} \right) \cr
& {\text{The range of the inverse function tangent is }} - \frac{\pi }{2} < x < \frac{\pi }{2} \cr
& {\text{Then for }}{\tan ^{ - 1}}\left( \theta \right){\text{ the value of }}\theta {\text{ is in }} - \frac{\pi }{2} < x < \frac{\pi }{2},{\text{ so}} \cr
& {\tan ^{ - 1}}\left( { - 1} \right) = - \frac{\pi }{4} \cr} $$
