Prove: tan(x-y)+tan(y-z)+tan(z-x)=tan(x-y) tan(y-z)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), 
since tan(x-y) = -tan(y-x).
Please put me as brainlest if it is correct