If $2 \tan^2 \theta - 4 \sec \theta + 3 = 0$,then $2 \sec \theta =$

If $\sin \theta + \text{cosec} \theta = 2$,the value of $\sin^{10} \theta + \text{cosec}^{10} \theta$ is

The number of all possible values of $\theta$,where $0 < \theta < \pi$,for which the system of equations
$(y+z) \cos 3\theta = (xyz) \sin 3\theta$
$x \sin 3\theta = \frac{2 \cos 3\theta}{y} + \frac{2 \sin 3\theta}{z}$
$(xyz) \sin 3\theta = (y+2z) \cos 3\theta + y \sin 3\theta$
have a solution $(x_0, y_0, z_0)$ with $y_0 z_0 \neq 0$,is

If $\cos \theta - \sin \theta = \sqrt{5} \sin \theta$,then $\cos \theta + \sin \theta = $

The sum $S = \sin \theta + \sin 2\theta + \dots + \sin n\theta$ equals

The value of $\csc \frac{\pi}{18} - \sqrt{3} \sec \frac{\pi}{18}$ is a