If $P(x) = x^3 + ax^2 + bx + c$ has roots $\alpha, \beta, \gamma$ such that $\alpha^2 + \beta^2 + \gamma^2 = 1$ and $\alpha^3 + \beta^3 + \gamma^3 = 3$, find $b$ given $\alpha+\beta+\gamma=0$.