Use the formulas and . These show that if then , and so . But if then . That gives the equation . The other two solutions will come from the other angles satisfying , namely and . (ThePerfectHacker had , but I think must be correct.)
(ThePerfectHacker had , but I think must be correct.)
Yes I made a mistake. But we are going to keep it secret.
The mistake was in the simplification. The solutions that I got to the depressed cubic are correct I just made mistakes in the identities.
Here is the corrected version: