Celebration problem marking the end of my exams

Geometry Level 4

If 3tan1(14)+tan1(120)=π4tan1(1x)3\tan^{-1}\left(\dfrac14 \right)+\tan^{-1}\left(\dfrac{1}{20} \right)=\dfrac{\pi}{4}-\tan^{-1}\left(\dfrac1x \right) , find xx to three decimal places.


This problem is part of my set: Geometry

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