What are the solutions to the equation on [0,2pi)?
sec (3x) = -2sqrt3/3
sec (3x) = -2√3 / 3 = -2 / √3
Note that if this is the sec(3x) then cos (3x) must be - √3/2
But cos (x) = - √3/2 at 5pi/6, 7pi/6 , 17pi/6, 19pi/6, 29pi/ 6, 31pi/ 6
Dividing each by 3 we get the solutions
5pi/18, 7pi/18, 17pi/ 18 , 19pi/18, 29pi/ 18, 31pi/ 18