If ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ then the general value of $\theta $ is

If $\cot \theta + \tan \theta = 2{\rm{cosec}}\theta $, the general value of $\theta $ is

If $\left| {\,\begin{array}{*{20}{c}}{\cos (A + B)}&{ - \sin (A + B)}&{\cos 2B}\\{\sin A}&{\cos A}&{\sin B}\\{ - \cos A}&{\sin A}&{\cos B}\end{array}\,} \right| = 0$, then $B =$

Find the general solution of the equation $\cos 3 x+\cos x-\cos 2 x=0$

Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta - cos\,2\theta  = 0$ and $2 \,cos^2\,\theta - 3\,sin\,\theta  = 0$ in the interval $[0, 2\pi ]$ is two.

Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta  - 3\,sin\,\theta  = 0$ in the interval $[0, \pi ]$ is two.

Let $\theta, 0 < \theta < \pi / 2$, be an angle such that the equation $x ^2+4 x \cos \theta+\cot \theta=0$ has equal roots for $x$. Then $\theta$ in radians is