The value of 2sin (12$$^\circ$$) $$-$$ sin (72$$^\circ$$) is :

The number of solutions of the equation

$$\cos \left( {x + {\pi \over 3}} \right)\cos \left( {{\pi \over 3} - x} \right) = {1 \over 4}{\cos ^2}2x$$, $$x \in [ - 3\pi ,3\pi ]$$ is :

Let $$S = \left\{ {\theta \in [ - \pi ,\pi ] - \left\{ { \pm \,\,{\pi \over 2}} \right\}:\sin \theta \tan \theta + \tan \theta = \sin 2\theta } \right\}$$.

If $$T = \sum\limits_{\theta \, \in \,S}^{} {\cos 2\theta } $$, then T + n(S) is equal to :