A solid glass sphere of refractive index $ n = \sqrt{3} $ and radius $ R $ contains a spherical air cavity of radius $ \dfrac{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 ____
