Grown pentagram

Algebra Level 3

If \(z_1 , z_2 , z_3 , z_4 \) are the roots of the equation \( z^4 + z^3 + z^2 + z^1 + 1 = 0\), then what the least value of \( \left \lfloor\ \left | z_1 + z_2 \right | \ \right \rfloor \)?

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