If $${\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3},$$     then the value of $${\text{1}} - {\text{2}}{\sin ^2}\theta $$   is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3} \cr & \Rightarrow \left( {{\text{co}}{{\text{s}}^2}\theta - {{\sin }^2}\theta } \right)\left( {{\text{co}}{{\text{s}}^2}\theta + {{\sin }^2}\theta } \right) = \frac{2}{3} \cr & \Rightarrow {\text{co}}{{\text{s}}^2}\theta - {\sin ^2}\theta = \frac{2}{3} \cr & \Rightarrow 1 - {\sin ^2}\theta - {\sin ^2}\theta = \frac{2}{3} \cr & \Rightarrow 1 - 2{\sin ^2}\theta = \frac{2}{3} \cr} $$