The minimum value of expression sinα+sinβ+sinγ where α,β,γ are positive real numbers satisfying α+β+γ=π

If singa+sinβ+sinγ=4cosα2+cosβ2+cosγ2 butα2+β2+γ2=π2 each of α2,β2,γ2 is less than π2; ∴cosα2,cosβ2,cosγ2 are +ve∴ minimum vlaue of 4cosα2,cosβ2,cosγ2 is +ve∴ the minimum value of sinα+sinβ+sinγ is +ve