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

The value of $$\cos 15^\circ \cos 7{1 \over 2}^\circ \sin 7{1 \over 2}^\circ $$ is

General solution of $$\sin x + \cos x = \mathop {\min }\limits_{a \in IR} \{ 1,{a^2} - 4a + 6\} $$ is

The value of $$\left( {1 + \cos {\pi \over 6}} \right)\left( {1 + \cos {\pi \over 3}} \right)\left( {1 + \cos {{2\pi } \over 3}} \right)\left( {1 + \cos {{7\pi } \over 6}} \right)$$ is