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If z1,z2,z3 satisfy the system of equati...

If `z_1,z_2,z_3` satisfy the system of equations given by `|z_1|=|z_2|=|z+3|=1,z_1+z_2+z_3=1 and z_1 z_2 z_3=1` such that `lm(z_1) < lm(z_2)< lm(z_3),` then find the value of `[|z_1+z_2^2+z_3^3|]` where `[ ]` denotes the greatest integer function.

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