If the \(m^{\text{th}\text{~}},n^{\text{th}\text{~}}\) and \(p^{\text{th}\text{~}}\) terms of an A.P and G.P. are equal and are \(x,y,z\) then prove that \(x^{y - z} \cdot y^{z - x} \cdot z^{x - y} = 1\)