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If |z(1)| = 1, |z(2)| =2, |z(3)|=3, and ...

If `|z_(1)| = 1, |z_(2)| =2, |z_(3)|=3, and |9z_(1)z_(2) + 4z_(1)z_(3)|= 12`, then find the value of `|z_(1) + z_(2) + z_(3)|`.

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