What are the solutions to the equation on [0,2π) ?

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