Arc Again And Tangent Again!

Geometry Level 2

arctan13+arctan14+arctan15+arctan1n=π4\arctan \dfrac{1}{3} + \arctan \dfrac{1}{4}+\arctan \dfrac{1}{5}+\arctan \dfrac{1}{n} = \dfrac{\pi}{4}

Find the positive integer nn such that the above equality is true.

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