$\begin{align}  & \sin \theta =-\tfrac{1}{2}\text{ for }0<\theta <{{360}^{o}} \\ & \sin \theta \text{ will be negetive in the 3rd and 4th quadrant} \\ & \sin \theta =-\tfrac{1}{2} \\ & \theta ={{\sin }^{-}}^{1}(-\tfrac{1}{2})={{30}^{o}} \\ & \text{But since it is negative }\theta =({{180}^{o}}+{{30}^{o}})\text{ or }({{360}^{o}}-{{30}^{o}}) \\ & \theta ={{210}^{o}}\text{ or }\theta ={{330}^{o}} \\\end{align}$