Sum of 10's a pie

Geometry Level 3

arctan⁡(13)+arctan⁡(14)+arctan⁡(15)+arctan⁡(1n)=π4\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 nn such that it satisfy the equation above.

Siddharth Bhatt by siddharth bhatt
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