To solve this equation, we can use the trigonometric identity:

sin^2(2x) - cos^2(2x) = -1
sin^2(2x) = 1 - cos^2(2x) (adding cos^2(2x) to both sides)
sin^2(2x) = sin^2(2x) (using the trigonometric identity sin^2(x) + cos^2(x) = 1)

Therefore, the equation is true for all values of x.