Complex roots of a 7th degree polynomial

Algebra Level 3

Consider the equation

x7+x6+x5+x4+x3+x2+x+1=0.x^7+x^6+x^5+x^4+x^3+x^2+x+1=0.

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

k=17[(xk)]2=?\sum_{k=1}^7{\big[\Re(x_k)\big]^2}=\, ?

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