21.(12分)已知函数 (x)=(sin )^2xsin 2x,-|||-(1)讨论f(x)在区间(0,π)的单调性;-|||-(2)证明: |f(x)|leqslant dfrac (3sqrt {3)}(8);-|||-(3)设 in (N)^* ,证明: (sin )^2x(sin )^22x(sin )^24x... (sin )^2(2)^nxleqslant dfrac ({3)^n}({4)^n}