Trigonometry identities

Geometry Level pending

\[\large 2\sin x+3\cos x =3\]

If real number \(x \in (0, \pi) \) satisfies the equation above and that \(\sin x = \dfrac ab\) and \(\cos x = \dfrac cb \), where \(a\), \(b\) and \(c\) are pairwise coprime positive integers. Find \(a+b+c\).

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