The equation $$\sqrt 3 \sin x + \cos x = 4$$ has

If $$\tan \left( {{{\alpha \pi } \over 4}} \right) = \cot \left( {{{\beta \pi } \over 4}} \right)$$ then

The principal value of $${\sin ^{ - 1}}\tan \left( { - {{5\pi } \over 4}} \right)$$ is

The value of $$\cos {\pi \over {15}}\cos {{2\pi } \over {15}}\cos {{4\pi } \over {15}}\cos {{8\pi } \over {15}}$$ is