Evaluate \(\lim \limits_{n \rightarrow \infty} \sum\limits_{k=1}^{n} \arctan \frac{2}{k^{2}}\). The answer is in the form of \(\frac{k}{m}\), where \(\frac{k}{m}\) is a simplified fraction. Please provide the value of \(k + m\).

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