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

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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