Let $a$, $b$, and $c$ be complex numbers such that $|a|=|b|=|c|=1$ and $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=-1$. Find all positive values of $|a+b+c|$.
The only possible value of |a + b + c| is 1. This happens when a = b = 1 and c = -1.
