If ( θ=-(1)/(2)) and ( θ=1 / 3 ), then (θ=)

We shall first consider values of (\theta) between 0 ($$\begin{aligned} & \text{ and } 2 \pi \sin \theta=-\frac{1}{2}=-\sin \frac{\pi}{6}=\sin \left(\pi+\frac{\pi}{6}\right) \\ & \text{ or } \sin (2 \pi-\pi / 6) \\ & \therefore \theta=7 \pi / 6 ; 11 \pi / 6 \\ & \tan \theta=1 / \sqrt{3}=\tan (\pi / 6) \text{ or } \tan (\pi+\pi / 6) \\ & \therefore \theta=\pi / 6,7 \pi / 6 \end{aligned}$$) The value of (\theta) which satisfies both the equations is (7 \pi / 6) Hence the general value of (\theta) is (2 n \pi+7 \pi / 6) where (\mathrm{n} \in $\mathrm{I}$)