$${\sec ^2}\theta = {{4xy} \over {{{\left( {x + y} \right)}^2}}}\,$$ is true if and only if

$$\,3{\left( {\sin x - \cos x} \right)^4} + 6{\left( {\sin x + \cos x} \right)^2} + 4\left( {{{\sin }^6}x + {{\cos }^6}x} \right) = $$

The general values of $$\theta $$ satisfying the equation $$2{\sin ^2}\theta - 3\sin \theta - 2 = 0$$ is

The minimum value of the expression $$\sin \,\alpha + \sin \,\beta \, + \sin \,\gamma ,\,$$ where $$\alpha ,\,\beta ,\,\gamma $$ are real numbers satisfying $$\alpha + \beta + \gamma = \pi $$ is