Sin2x (2cos2x-1) = cos2x (radical 3-2sin2x) x greater than or equal to 0 less than 2 π

Sin2x (2cos2x-1) = cos2x (radical 3-2sin2x) x greater than or equal to 0 less than 2 π

sin2x(2cos2x-1)=cos2x(√3-2sin2x)
2sin2xcos2x-sin2x=√3cos2x-2sin2xcos2x
4sin2xcos2x=√3cos2x+sin2x
2sin4x=2(√3/2*cos2x+1/2*sin2x)
sin4x=(sinπ/3*cos2x+cosπ/3*sin2x)
sin4x=sin(π/3+2x)
4X = 2K π + π / 3 + 2x or 4x = 2K π + π - (π / 3 + 2x)
From 4x = 2K π + π / 3 + 2x
x=kπ+π/6
When k = 0, x = π / 6; when k = 1, x = 7 π / 6; when k = 2, X is not in [0,2 π], so it is not considered
From 4x = 2K π + π - (π / 3 + 2x)
x=kπ/3+π/9
When k = 0, x = π / 9; when k = 1, x = 4 π / 9; when k = 2, x = 7 π / 9; when k = 3, x = 10 π / 9; when k = 4, x = 14 π / 9; when k = 5, x = 17 π / 9, k = 6, X is not in [0,2 π], so it is not considered
So the value of X can be π / 9, π / 6, 4 π / 9, 7 π / 9, 10 π / 9, 7 π / 6, 14 π / 9, 17 π / 9