Should be a good brain refresher!

$\displaystyle

{4-4\cos^2(x) \cdot \left(1-\frac{1}{\left(\csc^2(x)\right)}\right)^2}+(cot^2( 2x))\frac{(1-2\sin^2(x))^2}{\frac{1}{\frac{1+\cos(2x)}{\cos(2x) }\cdot \frac{1-\cos(2x)}{\cos(2x)}}}

$

The answer should come out to a really nice answer if I did my math right........ After a lot of editing, I hope this comes to the right answer (many mistakes)

THIS IS THE FINALIZED AND EDITED PROBLEM.