Sin^2 x + cos^2 2x + sin^2 3x=3/2

Sin^2x + cos^2 2x + sin^2 3x = 3/2

1 - cos2x + 1 + cos4x + 1 - cos6x = 3

cos4x - cos6x - cos2x = 0

cos 4x - (cos6x + cos 2x) = 0

cos4x - 2cos4xsin2x = 0;

cos4x (1 - 2sin2x) = 0;

cos4x = 0; 4x = π/2 + πn, n ∈ Z; x = π/8 + πn/4, n ∈ Z;

sin2x = 1/2; 2x = π/6 + πn, n ∈ Z; x = π/12 + πn/2, n ∈ Z;