Trigonometry

[UNknown 2010]

1. The problem statement, all variables and given/known data
Show that:
csc 2 + csc 4 + csc 8 + ...... + csc 1024 = cot 1 - cot 1024


2. Relevant equations
1+cot2x = csc2x


3. The attempt at a solution
I don't know how to start !!!!!!!!

[Dick]

The identity you really want is csc(2x)=cot(x)-cot(2x). Can you prove that and apply it?

[UNknown 2010]

I got it :)

Thanks a lot