Let S = {$$\theta $$ $$ \in $$ [–2$$\pi $$, 2$$\pi $$] : 2cos²$$\theta $$ + 3sin$$\theta $$ = 0}. Then the sum of the elements of S is

If cos($$\alpha $$ + $$\beta $$) = 3/5 ,sin ( $$\alpha $$ - $$\beta $$) = 5/13 and 0 < $$\alpha , \beta$$ < $$\pi \over 4$$, then tan(2$$\alpha $$) is equal to :

The maximum value of 3cos$$\theta $$ + 5sin $$\left( {\theta - {\pi \over 6}} \right)$$ for any real value of $$\theta $$ is :

The value of $$\cos {\pi \over {{2^2}}}.\cos {\pi \over {{2^3}}}\,.....\cos {\pi \over {{2^{10}}}}.\sin {\pi \over {{2^{10}}}}$$ is -