If $\mathrm{n}$ is the number of solutions of the equation

$2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$

and $S$ is the sum of all these solutions, then the ordered pair $(\mathrm{n}, \mathrm{S})$ is :

If $\theta $ and $\phi $ are acute satisfying $\sin \theta = \frac{1}{2},$ $\cos \phi = \frac{1}{3},$ then $\theta + \phi \in $

If $tan(\pi sin \theta)$ $= cot(\pi cos \theta)$, then $\left| {\cot \left( {\theta  - \frac{\pi }{4}} \right)} \right|$ is -

If $(2\cos x - 1)(3 + 2\cos x) = 0,\,0 \le x \le 2\pi $, then $x = $

If $1\,\, + \,\,\sin \theta \,\, + \,\,{\sin ^2}\theta  +  \ldots .\,\,to\,\,\infty \,\, = \,\,4\, + 2\sqrt 3 ,\,\,0\,\, < \,\theta \,\,\pi ,\,\,\theta \,\, \ne \,\frac{\pi }{2}\,,$ then $\theta  = $

The number of values of $x$ for which $sin2x + sin4x = 2$ is