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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 $a+b+c$ .