A value of $\theta$ for which $\frac{2+3i\sin\theta}{1-2i\sin\theta}$ is purely imaginary, is: (1) $\frac{\pi}{3}$ (2) $\frac{\pi}{6}$ (3) $\sin^{-1}\left(\frac{\sqrt{3}}{4}\right)$ (4) $\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)$
A value of $\theta$ for which $\frac{2+3i\sin\theta}{1-2i\sin\theta}$ is purely imaginary, is:
(1) $\frac{\pi}{3}$
(2) $\frac{\pi}{6}$
(3) $\sin^{-1}\left(\frac{\sqrt{3}}{4}\right)$
(4) $\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)$