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If 0<x1<x2<x3<pi, then prove that sin((x...

If 0<`x_1`<`x_2`<`x_3`<`pi`, then prove that `sin((x_1+x_2+x_3)/3)>(sinx_1+sinx_2+sinx_3)/3` . Hence or otherwise prove that if `A, B, C` are angles of a triangle, then the maximum value of `sinA+sinB+sinC` is `(3sqrt(3))/2`

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