Answer
$$0$$
Work Step by Step
$$\eqalign{
& \tan 3\pi \cr
& {\text{Write tan 3}}\pi {\text{ as tan}}\left( {2\pi + \pi } \right) \cr
& = {\text{tan}}\left( {2\pi + \pi } \right) \cr
& {\text{Use the identity tan}}\left( {A + B} \right) = \frac{{\tan A + \tan B}}{{1 - \tan A\tan B}} \cr
& {\text{tan}}\left( {2\pi + \pi } \right) = \frac{{\tan 2\pi + \tan \pi }}{{1 - \tan \left( {2\pi } \right)\tan \pi }} \cr
& {\text{Simplify}} \cr
& {\text{tan}}\left( {2\pi + \pi } \right) = \frac{{0 + 0}}{{1 - \left( 0 \right)\left( 0 \right)}} \cr
& {\text{tan}}\left( {2\pi + \pi } \right) = 0 \cr} $$
