Answer
$\theta = 30^{\circ}, 150^{\circ}, 270^{\circ}$
Work Step by Step
$sin~\theta-cos~2\theta = 0$
$sin~\theta-(1-2sin^2\theta) = 0$
$2sin^2\theta+sin~\theta-1 = 0$
$(2sin\theta-1)(sin~\theta+1) = 0$
$(2sin\theta-1) = 0$ or $(sin~\theta+1) = 0$
$sin~\theta = \frac{1}{2}$ or $sin~\theta = -1$
$\theta = 30^{\circ}, 150^{\circ}$ or $\theta = 270^{\circ}$
