\frac{1}{2^n}\cot{\frac{x}{2^n}}-\cot{x}+\frac{1}{2^{n+1}}\tan^{n+1}{\frac{x}{2^{n+1}}}=
\frac{1}{2^{n+1}}\cot{\frac{x}{2^{n+1}}}-\cot{x},