Answer
$\{0^{o}, 45^{o},135^{o}, 180^{o},225^{o},315^{o}\}$
Work Step by Step
.. subtract $ 2\tan\theta$ from both sides ...
$\sec^{2}\theta\tan\theta-2\tan\theta=0$
$\tan\theta(\sec^{2}\theta-2)=0$
... zero factor principle ...
1. $\quad \tan\theta =0 \ \Rightarrow\ \theta=0^{o}, 180^{o}$
or
2.$\quad \sec^{2}\theta=2 \ \Rightarrow\ \sec\theta=\pm\sqrt{2} \ \Rightarrow\ $
$\displaystyle \ \Rightarrow\ \cos\theta=\pm\frac{1}{\sqrt{2}}=\frac{\pm\sqrt{2}}{2}$
$\ \Rightarrow\ \theta=45^{o},135^{o},225^{o},315^{o}$
Solution set = $\{0^{o}, 45^{o},135^{o}, 180^{o},225^{o},315^{o}\}$
