If $\sin \alpha = \frac{{336}}{{625}}$ and $450^\circ < \alpha < 540^\circ ,$ then $\sin \left( {\frac{\alpha }{4}} \right) = $

If $\frac{x}{{\cos \theta }} = \frac{y}{{\cos \left( {\theta - \frac{{2\pi }}{3}} \right)}} = \frac{z}{{\cos \left( {\theta + \frac{{2\pi }}{3}} \right)}},$ then $x + y + z = $

For $A = 133^\circ ,\;2\cos \frac{A}{2}$ is equal to

If $2\sec 2\alpha = \tan \beta + \cot \beta ,$ then one of the values of $\alpha + \beta $ is

$1 - 2{\sin ^2}\left( {\frac{\pi }{4} + \theta } \right) = $

If $\alpha + \beta - \gamma = \pi ,$ then ${\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = $