# Are you ready for JEE-4?

Geometry Level 4

$\mathfrak{T}_n=\cot^{-1} 2+\cot^{-1} 8+\cot^{-1} 18+\cdots \cot^{-1} 2n^2$

$\displaystyle \lim_{n\to\infty}\mathfrak{T}_n=\dfrac{\color{red}{\alpha }\pi}{\color{blue}{\gamma}}$ where $$\color{red}{\alpha}$$ and $$\color{blue}{\gamma}$$ are coprime. $\Large \color{red}{\alpha} +4\color{blue}{\gamma}=\ ?$

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