Help finding a zero of function

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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?
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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