csc (3x) = -2√3/3 = -2/√3
This is the same as sin (3x) = -√3/2
Note that sin (x) = -√3/2 at (4/3)pi, (5/3)pi, (10/3)pi, (11/3)pi, (16/3)pi, (17/3)pi
Dividing each of these by 3 we get that
x = (4/9)pi, (5/9)pi, (10/9)pi, (11/9)pi, (16/9)pi, (17/9) pi