To solve this equation, we need to simplify it first.

First, we can rewrite cos^2(3x) as (cos(3x))^2 and sin^2(3x) as (sin(3x))^2.

Therefore, the equation becomes:

1/2 + (cos(3x))^2/2 - (sin(3x))^2/2 = 0

Now, we can combine the terms by finding a common denominator:

(1 + (cos(3x))^2 - (sin(3x))^2)/2 = 0

Now, we can use the trigonometric identity cos^2(x) + sin^2(x) = 1 to simplify this equation further:

(1 + 1)/2 = 0

2/2 = 0

1 = 0

Since this is not a true statement, there is no solution to this equation.