Evaluate the expression: $\tan \left(\arctan 2+\arctan \frac{2}{2^{2}}+\cdots+\arctan \frac{2}{12^{2}}\right)$. The original answer is in the form $-\frac{m}{n}$. Please provide the value of $m + n$.

Let's think step by step and output the final answer within \boxed{}.
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