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Geometry Level 4

Find the smallest possible positive value of θ\theta such that tan2(θ)=sec(θ). \tan^2(\theta)=\sec (\theta).

If θ\theta can be represented by tan1( a+bc )\tan^{-1}\left( \ \sqrt{\dfrac{a+\sqrt{b}}{c}}\ \right) where bb is square free and a,b,ca,b,c are integers. Find a+b+ca+b+c.

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