Solve: sin(2x) = √3cos(2x) for all values of x

Not sure how to do this one, tried factoring it equal to 0 but cannot get it thanks

sin(2x) = √3cos(2x)
sin(2x)/cos(2x) = √3
tan(2x) = √3
.....

sin(2x) = √3 cos(2x)
sin(2x) - √3 cos(2x) = 0
√3 = tan(π/3), therefore
sin(2x) - tan(π/3) cos(2x) = 0
Multiplying each side by cos(π/3):
sin(2x)cos(π/3) - sin(π/3) cos(2x) = 0
sin(2x - π/3) = 0
2x - π/3 = kπ
2x = π/3 + kπ
x = π/6 + kπ/2