\[sin^{-1} x = \frac{\pi}{2} - cos^{-1} x\]

\[tan^{-1} x = \frac{\pi}{2} - cot^{-1} x\]

\[sin^{-1} \theta = cos^{-1} \theta\]

\[sin^{-1} \theta = cos^{-1} \theta = \frac{\pi}{2} - sin^{-1} \theta\]

\[2sin^{-1} \theta = \frac{\pi}{2}\]

\[sin^{-1} \theta = \frac{\pi}{4}\]

\[\theta = sin(\frac{\pi}{4})= \frac{\sqrt{2}}{2}\]

\[5tan^{-1} \theta = 4 cot^{-1} \theta\]

\[5tan^{-1} \theta = 4cot^{-1} \theta =4( \frac{\pi}{2} - tan^{-1} \theta )=2 \pi - 4 tan^{-1} \theta\]

\[9tan^{-1} \theta = 2 \pi\]

\[tan^{-1} \theta = \frac{2 \pi}{9}\]

\[\theta = tan(\frac{2 \pi}{9})\]