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{\frac{3}{2}} and \sqrt{3}, \theta= \sin ^{-1} [\sqrt{\frac{3}{2}} \sin (\frac{\pi}{\beta}) ] , where the value of \beta is ______ . [JEE Adv 2024 P2]

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