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Consider the equation

$x^7+x^6+x^5+x^4+x^3+x^2+x+1=0.$

Let $x_k$ be the $k^\text{th}$ distinct root of the equation, and let $\Re(x_k)$ be the real part of that root. Then

$\sum_{k=1}^7{\big[\Re(x_k)\big]^2}=\, ?$

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