The sum of all values of $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ satisfying ${\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}$ is
$\pi $
$\frac{{5\pi }}{4}$
$\frac{{\pi }}{2}$
$\frac{{3\pi }}{8}$
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 = $
If $\cos 3\theta = \alpha \cos \theta + \beta {\cos ^3}\theta ,$ then $(\alpha ,\beta ) = $
If $3\cos \theta + 4\sin \theta = 5$ then $3\sin \theta - 4\cos \theta $ is
$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ = $
$\frac{{\cos 12^\circ - \sin 12^\circ }}{{\cos 12^\circ + \sin 12^\circ }} + \frac{{\sin 147^\circ }}{{\cos 147^\circ }} = $