Geometrical Optics

A light beam is travelling from Region I to Region IV
(Refer figure). The refractive index in Regions I, II, III and IV are \({n_0},{{{n_0}} \over 2},{{{n_0}} \over 6}\) and \({{{n_0}} \over 8}\), respectively. The angle of incidence \(\theta\) for which the beam just misses entering Region IV is