MathematicsMedium66×since 2002Q4118For α,β,γ≠0\alpha, \beta, \gamma \neq 0α,β,γ=0, if sin−1α+sin−1β+sin−1γ=π\sin ^{-1} \alpha+\sin ^{-1} \beta+\sin ^{-1} \gamma=\pisin−1α+sin−1β+sin−1γ=π and (α+β+γ)(α−γ+β)=3αβ(\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3 \alpha \beta(α+β+γ)(α−γ+β)=3αβ, then γ\gammaγ equalsA3\sqrt{3}3B32\frac{\sqrt{3}}{2}23C12\frac{1}{\sqrt{2}}21D3−122\frac{\sqrt{3}-1}{2 \sqrt{2}}223−1Check answerSkip