$\large \alpha + \beta + \gamma + \delta = \alpha^7 + \beta^7 + \gamma^7 + \delta^7 = 0$

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

The answer is 0.

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This is a tricky solution.

Choose $\alpha=\beta=\gamma=\beta=0$ , we have $\alpha(\alpha+\beta)(\alpha+\gamma)(\alpha+\delta)=0$