# 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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