I am preparing a paper on Huygens' approximations to pi and I have to prove the following inequality: if 0<= x>= pi/2 then

pi>= (pi/x)sin(x)(20+51cos(x)-2cos^2(x)+6cos^3(x))(21+18cos(x)+36cos^2(x))

The usual method of showing that the left hand side equals pi for x=0 and then trying to prove that it decreases for x>0 by proving that the derivative is negative is difficult since the derivative is quite complex.

I would appreciate any help.