Given, sin2x - sin4x + sin6x = 0

=> sin2x + sin6x - sin4x = 0

=> (sin2x + sin6x) - sin4x = 0

=> 2*sin {(2x + 6x)/2}*cos{(2x - 6x)/2} - sin4x = 0

=> 2*sin(4x)*cos(-2x) - sin4x = 0

=> 2*sin4x * cos2x - sin4x = 0

=> sin4x(2cos2x - 1) = 0

=> sin4x = 0 and 2cos2x - 1 = 0

=> 4x = nπ, n ∈ Z

=> x = nπ/4, n ∈ Z

and 2cos2x - 1 = 0

=> 2cos2x = 1

=> cos 2x = 1/2

=> cos 2x = cos π/3

=> 2x = 2nπ ± nπ/3, n ∈ Z

=> x = nπ ± nπ/6, n ∈ Z