If \( \left|\begin{array}{lll}(\beta+\gamma-\alpha-\delta)^{4} & (\beta+\gamma-\alpha-\delta)^{2...

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If \( \left|\begin{array}{lll}(\beta+\gamma-\alpha-\delta)^{4} & (\beta+\gamma-\alpha-\delta)^{2} & 1 \\ (\gamma+\alpha-\beta-\delta)^{4} & (\gamma+\alpha-\beta-\delta)^{2} & 1 \\ (\alpha+\beta-\gamma-\delta)^{4} & (\alpha+\beta-\gamma-\delta)^{2} & 1\end{array}\right| \) \( =-k(\alpha-\beta)(\alpha-\gamma)(\alpha-\delta)(\beta-\gamma)(\beta-\delta)(\gamma-\delta) \), then the value of \( k \) is
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