Let ABCD be a square of side of unit length. Let a circle C1centered 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  meet the side AB at E. If the length of EB is α+3β, where α, β are integers, then α+ β  is equal to _________