Is that a trig identity?

Geometry Level 3

\[\tan{2x} \tan{3x} \tan{5x} = \tan{Ax}-\tan{Bx}-\tan{Cx}\]

The above shows a trigonometric identity, where \(A,B,C\) are positive integers and \(A=B+C\), enter \(A+B+C\).

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