To solve this equation, we need to isolate the cosine function on one side of the equation.
First, we can rewrite the equation as:

1 + cot(2x) = 1 * cos(3π/2 - 2x)

Now, we know that cot(2x) = 1 / tan(2x) = cos(2x) / sin(2x)

Therefore, we can rewrite the equation as:

1 + cos(2x) / sin(2x) = cos(3π/2 - 2x)

Now, we need to use trigonometric identities to simplify the equation further.

We know that cos(3π/2 - 2x) = -sin(2x)

Now, substitute this value back into the equation:

1 + cos(2x) / sin(2x) = -sin(2x)

Now, multiply through by sin(2x) to clear the fraction:

sin(2x) + cos(2x) = -sin^2(2x)

Now, use the Pythagorean identity sin^2(2x) = 1 - cos^2(2x) to substitute back into the equation:

sin(2x) + cos(2x) = - (1 - cos^2(2x))

Now, expand the right side of the equation:

sin(2x) + cos(2x) = -1 + cos^2(2x)

Rearrange the equation to isolate cos(2x):

1 + sin(2x) = cos^2(2x)

Therefore, the final solution to the equation is 1 + sin(2x) = cos^2(2x).