A solid glass sphere of refractive index $$n = \sqrt{3}$$ and radius $$R$$ contains a spherical air cavity of radius $$\frac{R}{2}$$, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index $$n = 1$$) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source $$S$$ emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point O and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is $$\theta$$. The value of $$\sin \theta$$ is ________.