Number of solutions of the equation $2^x + x = 2^{sin \ x} +  \sin x$ in $[0,10\pi ]$ is -

If $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha $, then the general value of $\theta $ is

The number of values of $\alpha $ in $[0, 2\pi]$ for which $2\,{\sin ^3}\,\alpha  - 7\,{\sin ^2}\,\alpha  + 7\,\sin \,\alpha  = 2$ , is

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

Number of solutions of $8cosx$ = $x$ will be 

If ${\left( {\frac{{\sin \theta }}{{\sin \phi }}} \right)^2} = \frac{{\tan \theta }}{{\tan \phi }} = 3,$ then the value of $\theta $ and $\phi $ are