Let be a quadratic polynomial with complex coefficients whose coefficient is 1. Suppose the equation has four distinct solutions,

Let \(P(x)\) be a quadratic polynomial with complex coefficients whose \(x^2\) coefficient is 1. Suppose the equation \(P(P(x))=0\) has four distinct solutions, \(x=3,4,a,b\). Find the sum of all possible values of \((a+b)^2\).