Stuck with complex numbers

[diracy]

....

[eumyang]

Not all of the characters are appearing in my browser, so I had to guess what you wrote.

You need to express z3 two ways. One is to expand (cos θ + i sin θ)3 by multiplying the binomials out. The other is to use DeMoivre's Theorem. Since the two expressions are supposed to be equal, equate the real number portions and the imaginary number portions.