Grown pentagram

Algebra Level 3

If z1,z2,z3,z4z_1 , z_2 , z_3 , z_4 are the roots of the equation z4+z3+z2+z1+1=0 z^4 + z^3 + z^2 + z^1 + 1 = 0, then what the least value of  z1+z2  \left \lfloor\ \left | z_1 + z_2 \right | \ \right \rfloor ?

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