\(\tan \theta\) in Quadratic

Geometry Level pending

The following is a quadratic equation with rational coefficients: \[x^2-\left(\tan \theta + \frac{1}{\tan \theta}\right)x+1=0.\] If one of its roots is \(3-\sqrt{8},\) what is the value of \[\frac{1}{\sin \theta \cos \theta}?\]

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