The value of $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is $............$.

If $A + B + C = \frac{{3\pi }}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $

If $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ then :

$\frac{{\sin \theta + \sin 2\theta }}{{1 + \cos \theta + \cos 2\theta }} = $

Prove that $\frac{\sin x-\sin 3 x}{\sin ^{2} x-\cos ^{2} x}=2 \sin x$

$\tan {3^o} + 2\tan {6^o} + 4\tan {12^o} + 8\cot {24^o} = \cot {\theta ^o}$ then