Answer
$\theta \approx 1.107+\pi k$
$\theta \approx -1.107+\pi k$
$\theta =\dfrac {2\pi }{3}+2\pi k$
Work Step by Step
$\left( \tan ^{2}\theta -4\right) \left( 2\cos \theta +1\right) =0$
1)$
\left( \tan ^{2}\theta -4\right) =0\Rightarrow \tan \theta =\pm 2\Rightarrow \
$$\theta =\tan ^{-1}\left( 2\right) \Rightarrow \theta \approx 1.107+\pi k$
$\theta =\tan ^{-1}\left( -2\right) \Rightarrow \theta \approx -1.107+\pi k$
2)$2\cos \theta +1=0\Rightarrow \cos \theta =-\dfrac {1}{2}\Rightarrow \theta =\dfrac {2\pi }{3}+2\pi k$
