Answer
$\theta \approx 1.25+\pi k;$
$\theta \approx -1.25+\pi k$
$\theta \approx 1.107+\pi k$
$\theta \approx -1.107+\pi k$
Work Step by Step
$\left( \tan ^{2}\theta \right) ^{2}-13\tan ^{2}\theta +36=0$
$\tan ^{2}\theta =\dfrac {13\pm \sqrt {13^{2}-4\times 1\times 36}}{2}=\dfrac {13\pm 5}{2}=9;4 $
$\tan ^{2}\theta =9\Rightarrow \tan \theta =\pm 3\Rightarrow $
$\theta =\tan ^{-1}\left( 3\right) \approx 1.25+\pi k;$
$\theta =\tan ^{-1}\left( -3\right) \approx -1.25+\pi k$
$\tan ^{2}\theta =4\Rightarrow \tan \theta =\pm 2\Rightarrow $
$\theta =\tan ^{-1}\left( 2\right) \approx 1.107+\pi k$
$\theta =\tan ^{-1}\left( -2\right) \approx -1.107+\pi k$
