Answer
Solution set: $\{30^{o},210^{o},240^{o},300^{o}\}$
Work Step by Step
Using the zero product principle, either
1. $\quad \cot\theta-\sqrt{3}=0\quad$or
2. $\quad 2\sin+\sqrt{3=0.}$
1. $\quad \cot\theta=\sqrt{3}$
$\theta=30^{o}\quad$or $\theta=30^{0}+180^{o}=210^{o}$
$2.\quad 2\sin\theta=-\sqrt{3}\quad/\div 2$
$\displaystyle \sin\theta=-\frac{\sqrt{3}}{2}$
... use the unit circle, y coordinate = $-\displaystyle \frac{\sqrt{3}}{2}$...
$\theta=240^{o} \quad$ or $\theta=300^{o}$
Solution set: $\{30^{o},210^{o},240^{o},300^{o}\}$
