Let $g(x)=f(x)+f(1-x)$ and $f^{\prime \prime}(x)>0, x \in(0,1)$,
If $g$ is decreasing in the interval ( $0, \alpha$ ) and increasing in the interval ( $\alpha, 1$ ), then $\tan ^1(2 \alpha)+\tan ^{-1}\left(\frac{1}{a}\right)+\tan ^{-1}\left(\frac{\alpha+1}{\alpha}\right)$ is equal to :
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