To solve the equation sin(3x) - sin(x) = 2cos(2x), we can use the trigonometric identity sin(3x) = 3sin(x) - 4sin^3(x) and cos(2x) = 1 - 2sin^2(x).

Substitute these identities into the equation:

3sin(x) - 4sin^3(x) - sin(x) = 2(1 - 2sin^2(x))
2sin(x) - 4sin^3(x) = 2 - 4sin^2(x)

Rearranging the terms:

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

Now, we can rewrite this equation in terms of sin(x) as:

2sin(x)(2sin^2(x) - 2sin(x) + 1) - 2(1) = 0

Factor out a 2sin(x):
2sin(x)(2sin^2(x) - 2sin(x) + 1) = 1

Set each factor to zero:

2sin(x) = 1 or 2sin^2(x) - 2sin(x) + 1 = 0

Solve the first equation:
sin(x) = 1/2
x = π/6

For the second equation, we can rewrite it as:

(2sin(x) - 1)^2 = 0
2sin(x) - 1 = 0
sin(x) = 1/2
x = π/6

Therefore, the solution to the equation sin(3x) - sin(x) = 2cos(2x) is x = π/6.