For α, β, γ ≠ 0, if sin^-1 α+ sin^-1 β+ sin^-1 γ=π and (α+β+γ)(α-γ+β)=3 α β, then γ equals

For $\displaystyle \alpha, \beta, \gamma \neq 0$, if $\displaystyle \sin ^{-1} \alpha+\sin ^{-1} \beta+\sin ^{-1} \gamma=\pi$ and $\displaystyle (\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3 \alpha \beta$, then $\displaystyle \gamma$ equals