Help finding a zero of function

[wildcat12]

Homework Statement

I need to find all the zeros of the function f(x)=cos(x)+3cos(3x) on the interval (-pi, pi)

Homework Equations

The Attempt at a Solution

i have found zeros at -pi, -pi/2, 0. pi/2, and pi. Looking at the graph i can see more zeros but i cannot figure out what they are! Anybody know how i can factor this or anything?

 

[Mentallic]

Do you know how to expand cos(3x) into powers of cos(x)?