You can use the quadratic formula to find a and b (alpha and beta).

x=(-B+-sqrt(B^2-4AC))/2A, so x=(-pi+-sqrt(pi^2-4sqrt(2)))/2=tan(angle).

The two possible values of arctan(x) are -.4986 and -1.2032 in radians.

Simply plug these values in for a and b in the second equation.