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Find the smallest possible positive value of θ\thetaθ such that tan2(θ)=sec(θ). \tan^2(\theta)=\sec (\theta).tan2(θ)=sec(θ).
If θ\thetaθ can be represented by tan−1( a+bc )\tan^{-1}\left( \ \sqrt{\dfrac{a+\sqrt{b}}{c}}\ \right)tan−1( ca+b ) where bbb is square free and a,b,ca,b,ca,b,c are integers. Find a+b+ca+b+ca+b+c.
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