Two equilateral-triangular prisms \(P_1\) and \(P_2\) are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism \(P_1\) at an angle of incidence \(\theta\) such that the outgoing ray undergoes minimum deviation in prism \(P_2\). If the respective refractive indices of \(P_1\) and \(P_2\) are \(\sqrt{3}/\sqrt{2})\) and \(\sqrt{3}\), then \(\theta = \sin^{-1}\left(\sqrt{3}/\sqrt{2}) \sin\left(\frac{\pi}{\beta}\right)\right)\), where the value of \(\beta\) is \_\_\_\_.
\includegraphics[width=0.5\linewidth]{p11.png}