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 $$\sqrt{\dfrac{3}{2}}$$ and $$\sqrt{3}$$, $$\theta = \sin^{-1}\left[\sqrt{\dfrac{3}{2}} \sin\left(\dfrac{\pi}{\beta}\right)\right]$$, where the value of $$\beta$$ is ________.