Tan(x-y)+tan(y-z)+tan(z-x):::tan(x-y)tan(y-x)tan(z-x)

tan(z-x) = tan((y-x)-(y-z)) => tan(z-x) = (tan(y-x) - tan(y-z))/(1+tan(y-x).tan(y-z)) by given formula. Multiply both sides by (1+tan(y-x).tan(y-z)): tan(z-x).(1+tan(y-x).tan(y-z)) = tan(y-x)-tan(y-z) => -tan(y-x) + tan(y-z) + tan(z-x) = -tan(y-x).tan(y-z).tan(z-x) => tan(x-y) + tan(y-z) + tan(z-x) = tan(x-y).tan(y-z).tan(z-x)