If sum of all the solutions of the equation

$$8\cos x.\left( {\cos \left( {{\pi \over 6} + x} \right).\cos \left( {{\pi \over 6} - x} \right) - {1 \over 2}} \right) = 1$$

in [0, $$\pi $$] is k$$\pi $$, then k is equal to

The number of solutions of sin3x = cos 2x, in the interval $$\left( {{\pi \over 2},\pi } \right)$$ is :

The number of x $$ \in $$ [0,   2$$\pi $$ ] for which

$$\left| {\sqrt {2{{\sin }^4}x + 18{{\cos }^2}x} - \sqrt {2{{\cos }^4}x + 18{{\sin }^2}x} } \right| = 1$$ is :

If $$0 \le x < 2\pi $$, then the number of real values of $$x$$, which satisfy the equation $$\,\cos x + \cos 2x + \cos 3x + \cos 4x = 0$$ is: