I solved for the answers, but I just want to know if I am correct or not. Thank you! 😀
No, not correct.
Fourth roots, so the angles should be 360/4 = 90 degrees apart.
The four roots shouold occupy the four vertices of a square.
12^(1/4) part is correct
Angles should be 90° apart = pi/2
Calculation of angle, θ = arctan (6sqrt (3) / 6) = arctan ( sqrt (3)) = pi/3
1st angle = ( θ/4) = (pi/3)/4 = pi/12
2nd angle= pi/12 + pi/2 = 7pi/12
3rd angle = 7pi/12 + pi/2 = 13pi/12
4th angle = 13pi/12 + pi/2 = 19pi/12