Answer
$\frac{\pi}{4}+k\pi$, $-1.25+k\pi$
Work Step by Step
$2\tan \theta+\sec^2\theta=4$
$2\tan \theta+\tan^2\theta+1=4$
$\tan^2\theta+2\tan \theta-3=0$
$(\tan\theta-1)(\tan \theta+3)=0$
If $\tan \theta-1=0$, then $\tan \theta=1$, and $\theta=\frac{\pi}{4}+k\pi$.
If $\tan \theta+3=0$, then $\tan \theta=-3$, and $\theta=-1.25+k\pi$.
