If $\cos ^{-1} 2 x+\cos ^{-1} 3 x=\frac{\pi}{3}$ and $4 x^2=\frac{a}{b}$, then $a+b$ is equal to

If $\theta=\sec ^{-1}(\cosh u)$, then $u=$

If $\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=k$, then $\sin ^{-1}\left(\sqrt{\frac{k}{2}}\right)+\cos ^{-1}\left(\frac{k}{3}\right)=$

$$4 \tan ^{-1} \frac{1}{5}-\tan ^{-1} \frac{1}{70}+\tan ^{-1} \frac{1}{99}=$$