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(C) Given that $\alpha + \beta + \gamma = \pi$. For a triangle with angles $\alpha, \beta, \gamma$,the sum of the sines of the angles is given by $\si

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(C) Given that $\alpha + \beta + \gamma = \pi$. For a triangle with angles $\alpha, \beta, \gamma$,the sum of the sines of the angles is given by $\sin \alpha + \sin \beta + \sin \gamma = 4 \cos(\alpha/2) \cos(\beta/2) \cos(\gamma/2)$. Since $\alpha, \beta, \gamma$ are angles of a triangle (or satisfy the sum condition),they must be in the interval $(0, \pi)$. Consequently,$\alpha/2, \beta/2, \gamma/2$ are in the interval $(0, \pi/2)$. In the interval $(0, \pi/2)$,the cosine function is always positive. Therefore,$4 \cos(\alpha/2) \cos(\beta/2) \cos(\gamma/2) > 0$. Thus,the expression $\sin \alpha + \sin \beta + \sin \gamma$ is always positive.

$\alpha, \beta, \gamma$ are real numbers satisfying $\alpha + \beta + \gamma = \pi$. The minimum value of the expression $\sin \alpha + \sin \beta + \sin \gamma$ is

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