To solve the equation sin(3x) - √3cos(3x) - 2sin(2x) = 0, we can use trigonometric identities to simplify the equation.

First, let's rewrite the equation using the double-angle formula for sine:

sin(3x) - √3cos(3x) - 2(2sin(x)cos(x)) = 0

Next, let's use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to eliminate the cosine term:

sin(3x) - √3(√1 - sin^2(x)) - 4sin(x)cos(x) = 0

sin(3x) - √3(1 - sin^2(x)) - 4sin(x)cos(x) = 0

sin(3x) - √3 + √3sin^2(x) - 4sin(x)cos(x) = 0

Now, let's use the double-angle formula for cosine:

sin(3x) - √3 + √3sin^2(x) - 4sin(x)(1 - 2sin^2(x)) = 0

sin(3x) - √3 + √3sin^2(x) - 4sin(x) + 8sin^3(x) = 0

Rearranging the terms:

8sin^3(x) + √3sin^2(x) - 4sin(x) + sin(3x) - √3 = 0

Now, we have a cubic equation in terms of sin(x). To solve this equation, we can use numerical methods or approximation techniques.