A monochromatic light is incident from air on a refracting surface of a prism of angle $$75^\circ$$ and refractive index $$n_0 = \sqrt 3$$. The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $$\theta \leq 60^\circ$$. The value of $$n^2$$ is ___________ .