The number of solutions of the equation $$\sin x = {\cos ^2}x$$ in the interval (0, 10) is _________.

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 ___________.

If $${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin (10^\circ )$$, then $$16 + {\alpha ^{ - 1}}$$ is equal to __________.