+1364 Let $a,$ $b,$ $c$ be complex numbers such that
\begin{align*}
\frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b} &= 0, \\
\frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b} &= 1, \\
\frac{a^3}{b + c} + \frac{b^3}{c + a} + \frac{c^3}{a + b} &= 2.
\end{align*}
Find $abc.$
