The equation $\cos ^{-1}(1-x)-2 \cos ^{-1} x=\frac{\pi}{2}$ has

$$ \tan \left(2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)\right)= $$

$$ \tanh ^{-1}\left(\frac{1}{3}\right)+\operatorname{coth}^{-1}(3)= $$

If $y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ and $\left(\frac{d^2 y}{d x^2}\right)_{x=2}=k$, then $25 k=$