3.8: Normal to sine curve and triangle OAB

The normal to the curve $y = \mathrm{sin}(4x - \pi)$ at the point $A(a, 0)$, where $\dfrac{\pi}{2} < a < \pi$, meets the $y$-axis at the point $B$. Find the exact area of triangle $OAB$, where $O$ is the origin.