Celebration problem marking the end of my exams

Geometry Level 4

If \[3\tan^{-1}\left(\frac14 \right)+\tan^{-1}\left(\frac{1}{20} \right)=\frac{\pi}{4}-\tan^{-1}\left(\frac1x \right) \]

Find \(x\) upto three decimal places.


This problem is part of my set: Geometry

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