I've got something like this:

I need to find $\displaystyle s$ that makes the following inequality true.

$\displaystyle \displaystyle\left|\frac{6s\cos x +1 - 6s}{-2s(\cos x -1) + 1}\right|\le 1$

Using some trig identities I got it down to $\displaystyle -4s\sin^2(x/2)-2\le -12s\sin^2(x/2)\le 4s\sin^2(x/2)$

which I think is correct, but I don't know what to do now...