1966 IMO Problems/Problem 4

Solution

Assume that \frac{1}{\sin{2x}}+\frac{1}{\sin{4x}}+\dots+\frac{1}{\sin{2^{n}x}}=\cot{x}-\cot{2^{n}x is true, then we use n=1\cot x - \cot 2x = \frac {1}{\sin 2x}