Well, then, what do you get? You see where "cot^3(x)" and "tan^3(x)" come from, don't you. So I guess your question would be "where did all the other terms go?" There are, in fact, four other terms: cot(x) times 1 and times tan^2(x) and -tan(x) times cot^2(x) and times 1. What do those give?
You know that "cot(x)tan(x)= 1", don't you?