Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x  \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-
 

The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{n \pi}{5}$ for $n=0, \pm 1, \pm 2$ and $\tan \theta=\cot 5 \theta$ as well as $\sin 2 \theta=\cos 4 \theta$ is

The number of solutions that the equation $sin5\theta cos3\theta  = sin9\theta cos7\theta $ has in $\left[ {0,\frac{\pi }{4}} \right]$ is

If $\cot (\alpha + \beta ) = 0,$ then $\sin (\alpha + 2\beta ) = $

If $\sin 2\theta = \cos 3\theta $ and $\theta $ is an acute angle, then $\sin \theta $ is equal to

If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is