Ok so the problem is as follows:

Find all real number solutions y of:

e^(iy) + e^(2iy) + e^(3iy)=0

Firstly I tried letting e^(iy) equal some variable X. Then:

X + X^2 + X^3=0 ==> X(1 + X + X^2)=0.

I used the quadratic formula on (1 + X + X^2) to get X=-1/2 ± (sqrt(3)/2)*i

So e^(iy)=-1/2 ± (sqrt(3)/2)*i

Where do I go from here? Am I even on the right track? Any help much appreciated!