Sum of 10's a pie

Geometry Level 3

\[\arctan\left(\frac {1}{3} \right)+ \arctan\left(\frac {1}{4}\right) + \arctan\left(\frac {1}{5} \right)+ \arctan\left(\frac {1}{n} \right)= \frac {\pi}{4}\]

Find the positive integer \(n\) such that it satisfy the equation above.

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