$\sin ^{-1}\left(\frac{\alpha}{17}\right)=-\cos ^{4}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{77}{36}\right)$ Let $\cos ^{-1}\left(\frac{4}{5}\right)=p$ and $\tan ^{-1}\left(\frac{77}{36}\right)=q$ $\Rightarrow \sin \left(\sin ^{-1} \frac{\alpha}{17}\right)=\sin (q-p)$ $=\sin q \cdot \cos p-\cos q \cdot \sin p$ $\Rightarrow \frac{\alpha}{17}=\frac{77}{85} \cdot \frac{4}{5}-\frac{36}{85} \cdot \frac{3}{5}$ $\Rightarrow \alpha=\frac{200}{25}=8$ $\sin ^{-1} \sin 8+\cos ^{-1} \cos 8$ $= -8+3 \pi+8-2 \pi$ $=\pi$