# $$\tan \theta$$ in Quadratic

Geometry Level 1

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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