Inverse Trigonometric Series

Geometry Level 4

\[\large \sum_{n=0}^{10} \text{arccot} \dfrac{1+2^{2n+1}}{2^n} = \text{arccot} \dfrac ab \]

If the equation above holds true for coprime positive integers \(a\) and \(b\), find \( \log_2 \dfrac{b+a}{a-b} \).

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