I don't know if this is right, but it seems like it...
Assuming you know how to do the n =1, n=k and n=k+1 ...
= -(k+1) +cot(theta)tan(k+1)(theta) + tan(k+1)tan (k+2) (theta)
= -(k+2)+ cot(theta)tan(k+1)(theta)+1+tan(k+1)(theta)tan(k+2)(theta)
= -(k+2) +cot(theta) tan (k+1)(theta)...
I don't know.
I was told, if you came last in a subject, and in the HSC exam, whoever comes last in that exam, that mark will go to you.
For your sake, I hope that's not the case.