Prove: tan(x-y)+tan(y-z)+tan(z-x)=tan(x-y) tan(y-z)tan(z-x) i need very good explanations because i can't do or understand this

Aresearcher believes increased perceived control influence the well-being of residents at a nursing home. to test this , she allowed one group of residents to have control over their daily lies, (where to eat etc) . the other group of 5 residents had these deceisions made by staff. the resident's feelings of well-being were measured on a 10 point scale at the end of a one month trial period. is there a difference on well-being?