Precise Carving

Geometry Level 4

\[\large \tan ^{-1} \left( \dfrac 34 \right) -2 \tan ^{-1} \left( \dfrac 15 \right) = \cos ^{-1} \left(\dfrac cd \right) \]

The equation above holds true for coprime positive integers \(c\) and \(d\). Find \(c+d\).

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