Let $$ABC$$ be a triangle and let $$D$$ be a point on the segment $$BC$$ such that $$AD=BC$$. Suppose $$\angle CAD=x^{\circ}$$, $$\angle ABC=y^{\circ}$$ and $$\angle ACB=z^{\circ}$$ and $$x, y, z$$ are in an arithmetic progression in that order where the first term and the common difference are positive integers. Find the largest possible value of $$\angle ABC$$ in degrees.