Trignometric limit

Calculus Level 3

\[ \displaystyle \lim _{ n\rightarrow \infty }{ \frac { \displaystyle \sum _{ r=1 }^{ { 2 }^{ n-1 }-1 }{ \tan ^{ 2 }{ \left (\frac { r\pi }{ { 2 }^{ n } } \right ) } } }{ { 4 }^{ n } } } \]

For positive integer \(n\), the limit evaluates to \( \dfrac a b\) for coprime positive integers \(a,b\). What is the value of \(a+b\)?

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