Circular functions help

[Mieow]

Consider the function f(x) =
Find the x-intercepts.

I can only get -17pi/18 and -5pi/18. I got -11pi/18 too but that was wrong

[nhmn0301]

Since you nearly get the right answer, I'll just jump straight to the step that might have cause some errors:
sec (3x - pi) = 2/*sqrt*3
3x - pi = -pi/6, -11pi/6
3x= 5pi/6, -5pi/6     (since 5pi/6 is out of the domain, I'll change it in the next step)
3x = -7pi/6, -5pi/6
x= -7pi/18, -5pi/18     
x= -7pi/18, -5pi/18, -19pi/18, -17pi/18  (adding the period of the graph, which is 2pi/3)
Hence, x = -7pi/18, -5pi/18 and -17pi/18  ( I have eliminated -19pi/18 since it is out of the domain)