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Algebra Level 2

α+β+γ+δ=α7+β7+γ7+δ7=0\large \alpha + \beta + \gamma + \delta = \alpha^7 + \beta^7 + \gamma^7 + \delta^7 = 0

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

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