To solve the equation cos(2x) = cos(6x), we can use the cosine angle addition formula, which states that cos(a + b) = cos(a)cos(b) - sin(a)sin(b).

So, let's rewrite the equation in terms of cos(2x) and cos(6x):

cos(2x) = cos(6x)
cos(2x) - cos(6x) = 0

Now, using the angle addition formula, we get:

cos(2x) - cos(2x)cos(4x) + sin(2x)sin(4x) = 0

Now, let's simplify this equation further by using the double angle formulas for cosine and sine:

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

Now, we have a quadratic equation in terms of cos(2x). Let cos(2x) = y:

y - 2y^2 + y - 2y^2(2 sqrt(1 - y^2)) = 0
y - 2y^2 + y - 2y^2(2 sqrt(1 - y^2)) = 0

Now, we can solve this equation for y (cos(2x)) to find the possible solutions for x.