Abstract
The system of unoriented tangle equations [Formula: see text] and [Formula: see text] is completely solved for the tangles U and [Formula: see text] as a function of [Formula: see text] where K1 and K2 are 4-plats, and [Formula: see text] and [Formula: see text] rational tangles such that |f1g2 - g1f2| > 1.
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