sec (3x) = -2√3/3 = -2√3
Note that this is the same as cos (3x) = ( -√3 / 2)
Note that cos (x) = -√3/2 at (5/6)pi , (7/6)pi , (17/6)pi, (19/6)pi , (29/6)pi, (31/6)pi
Divide each of these by 3 and we have
x = (5/18)pi, (7/18)pi ( 17/18)pi , (19/18)pi , (29/18)pi, (31/18)pi