Answer
$\theta = 30^{\circ}, 240^{\circ}, 240^{\circ}, 300^{\circ}$
Work Step by Step
$(\cot \theta- \sqrt 3)(2\sin \theta+ \sqrt 3) = 0$
$\cot \theta - \sqrt 3= 0$
$\cot \theta = \sqrt 3$
$\frac{1}{\tan \theta} = \sqrt 3$
$1 = \tan \theta \sqrt 3$
$\tan \theta = \frac{1}{\sqrt 3}$
$\tan \theta = \frac{\sqrt 3}{3}$
$\theta = 30^{\circ}, 240^{\circ}$
$2\sin \theta + \sqrt 3 = 0$
$2\sin \theta = - \sqrt 3$
$\sin \theta = - \frac{\sqrt 3}{2}$
$\theta = 240^{\circ}, 300^{\circ}$
Therefore, $\theta = 30^{\circ}, 240^{\circ}, 240^{\circ}, 300^{\circ}$
