Answer
$\theta =\pi +2\pi k$
$\theta =2\pi k$
$\theta =\dfrac {3\pi }{4}+\pi k$
Work Step by Step
$\tan \theta \sin \theta +\sin \theta =0\Rightarrow \sin \theta \left( \tan \theta +1\right) =0$
$\sin \theta =0\Rightarrow \theta =\sin ^{-1}\left( 0\right) =\pi +2\pi k;\theta =2\pi k$
$\left( \tan \theta +1\right) =0\Rightarrow \theta =\tan ^{-1}\left( -1\right) =\dfrac {3\pi }{4}+\pi k$
