\[\large I_{n} = \int_{0}^{\frac{\pi}{4}} \tan ^{n}x \, dx\]

We define the integral as above. And define the relation \( f(n) = \dfrac{1}{I_{n-2} - I_{n+2}} \). Evaluate the summation below.

\[ \large 2\sum_{r=2}^{10} f(r) \]

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