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Geometry Level 4

Find the smallest possible positive value of \(\theta\) such that \[ \tan^2(\theta)=\sec (\theta).\]

If \(\theta\) can be represented by \(\tan^{-1}\left( \ \sqrt{\dfrac{a+\sqrt{b}}{c}}\ \right)\) where \(b\) is square free and \(a,b,c\) are integers. Find \(a+b+c\).