If A + B + C = 180$$^\circ$$, then what is $$\sin 2A - \sin 2B - \sin 2C$$ equal to?

A is an angle in the fourth quadrant it satisfies the trigonometric equation $$3{(3 - {\tan ^2}A - \cot A)^2} = 1$$. Which one of the following is a value of A?

What is/are the solution(s) of the trigonometric equation $$\cos ec\,x + \cos x = \sqrt 3 $$ where 0 < x < 2$$\pi$$ ?

If $$\theta = {\pi \over 8}$$, then what is the value of $${(2\cos \theta + 1)^{10}}{(2\cos 2\theta - 1)^{10}}{(2\cos \theta - 1)^{10}}{(2\cos 4\theta - 1)^{10}}$$ ?