Maximum value in triangle

Geometry Level 4

\(A\), \(B\) and \(C\) are 3 angles of the triangle \(ABC\) such that \[\cos { 2A } +\cos { 2B } +\cos { 2C } \ge -1.\]

What is the maximum value of \( \sin { A } +\sin { B } +\sin { C }\)?

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