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Algebra Level 3

Let \(x, y,\) and \( z\) be lengths of the sides of a triangle such that \(x + y + z = 2\).

The range of \( xy + yz + zx - xyz \) is \( (m, n ] \).

If \(m+n = \frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?

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