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Geometry Level 4

\[\frac{\sqrt{3}-1}{\sin\nu}+\frac{\sqrt{3}+1}{\cos\nu}=4\sqrt{2}\] If \(ω_{1},ω_{2}\) are values of \(\nu\) satisfying the above equations. \(\nu\) belongs to \((0,90°)\) , then find \(|ω_{1}-ω_{2}|\).

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