At the interface between two materials having refractive indices n₁ and n₂, the critical angle for reflection of an em wave is ${\mathrm{\theta }}_{1\mathrm{c}}$. The n₂ material is replaced by another material having refractive index n₃, such that the critical angle at the interface between n₁ and n₃ materials is ${\mathrm{\theta }}_{2\mathrm{c}}$. If n₃ > n₂ > n₁; $\frac{{\mathrm{n}}_2}{{\mathrm{n}}_3}=\frac{2}{5}$ and $\sin {\mathrm{\theta }}_{1\mathrm{C}}-\sin {\mathrm{\theta }}_{2\mathrm{C}}=\frac{1}{2}$, then ${\mathrm{\theta }}_{1\mathrm{c}}$ is