Let ABCD be a square of side of unit length. Let a circle C₁ centered at A with unit radius is drawn. Another circle C₂ which touches C₁ and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle C₂ meet the side AB at E. If the length of EB is $$\alpha$$ + $${\sqrt 3 }$$ $$\beta$$, where $$\alpha$$, $$\beta$$ are integers, then $$\alpha$$ + $$\beta$$ is equal to ____________.