Answer
$\theta \approx 1.107+\pi k$
$\theta \approx 0.253+2\pi k$
$\theta \approx -0.253+2\pi k$
Work Step by Step
$\left( \tan \theta -2\right) \left( 16\sin ^{2}\theta -1\right) =0$
$\left( \tan \theta -2\right) =0\Rightarrow \theta =\tan ^{-1}\left( 2\right) \approx 1.107+\pi k$
$16\sin ^{2}\theta -1=0\Rightarrow \sin \theta =\pm \dfrac {1}{4}\Rightarrow \theta =\sin ^{-1}\left( \pm \dfrac {1}{4}\right) +2\pi k\approx \pm 0.253+2\pi k$
