Chapter 5 - Inner Product Spaces - 5.1 Definition of an Inner Product Space - Problems - Page 350: 3

$\theta=\cos^{-1}(\dfrac{\sqrt 6}{\pi})$

Let us consider that $\theta$ be an angle between the vectors $f$ and $g$, which can be written as: $\cos \theta=\dfrac{\langle f,g\rangle}{\|g\|\|g\|}$ Since, we have $\cos \theta=\dfrac{\pi}{(\sqrt {\dfrac{\pi}{2}})(\pi \sqrt {\dfrac{\pi}{3}}}=\dfrac{\sqrt 6}{\pi}$ So, the angle between $f$ and $g$ is equal to $\theta=\cos^{-1}(\dfrac{\sqrt 6}{\pi})$