Plenty of Integrate by Parts Part 2?

Calculus Level 5

You are given that $\displaystyle \int_0^\infty \frac { \sin x}{x} \, d x = \frac {\pi}{2}.$ If the value of $\displaystyle \int_0^\infty \frac { \sin^8 x}{x^4} \, dx$ is equal to $\dfrac ab\pi$ for coprime positive integers $a$ and $b$ . What is the value of $a+b$ ?