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Algebra Level 2

\[\large \alpha + \beta + \gamma + \delta = \alpha^7 + \beta^7 + \gamma^7 + \delta^7 = 0 \]

Suppose \(\alpha, \beta, \gamma \) and \(\delta\) are real numbers satisfying the equation above, find \(\alpha(\alpha + \beta)(\alpha + \gamma)(\alpha + \delta) \).

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