Method to solve a system of nonlinear equations

Question

Suppose that I have the following system, $$ \begin{equation} \left\{\begin{array}{lcl} a + b + c + d & = & \alpha \\ a^2 + b^2 + c^2 + d^2 & = & \beta \\ a^3 + b^3 + c^3 + d^3& = & \gamma \\ a^4 + b^4 + c^4 + d^4& = & \theta \end{array}\right. \end{equation} $$ in which I know that $\alpha, \beta, \gamma$ are positive, $\alpha=1$, $\beta<1$, $\gamma<1$, and $\theta<1$. If I know the values of $\beta$, $\gamma$, and $\theta$, how can I find $a, b, c, d$? Can someone tell me if there is a method to solve this? Which system of equations is this one? Does this have a specific name?