Answer
$\theta=\{30^o,150^o\}$
Work Step by Step
$sec(\theta)-2tan(\theta)=0$
$\frac{1}{cos(\theta)}-2\frac{sin(\theta)}{cos(\theta)}=0\;\;\;\;\;\;\;\;\;\;$ multiply each side by $cos(\theta)$.
$1-2sin(\theta)=0$
$-2sin(\Theta )=-1\;\;\;\;\;\;\;\;\;\;$ subtract $ 1 $ from each side.
$sin(\Theta )=\frac{-1}{-2} \;\;\;\;\;\;\;\;\;\;\;$ divide each side by $ -2 $
$sin(\Theta )=\frac{1}{2}$
$\theta= sin^{-1}(\frac{1}{2})$
We know $ sin(\theta) $ is positive in quadrant $I$ and quadrant $II$
$\theta=30^o\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\theta=180^o-30^o=150^o$
$\theta=30^o\;\;\;\;\;\;\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\;\;\;\theta=150^o$
$\theta=\{30^o,150^o\}$
