The number of elements in the set $$S = \{ \theta \in [ - 4\pi ,4\pi ]:3{\cos ^2}2\theta + 6\cos 2\theta - 10{\cos ^2}\theta + 5 = 0\} $$ is __________.

The number of solutions of the equation

$$2\theta - {\cos ^2}\theta + \sqrt 2 = 0$$ in R is equal to ___________.

The number of values of x in the interval $$\left( {{\pi \over 4},{{7\pi } \over 4}} \right)$$ for which

$$14\cos e{c^2}x - 2{\sin ^2}x = 21 - 4{\cos ^2}x$$ holds, is ____________.