= Sinc fourth-power integral
{title2=$\displaystyle\int_0^\infty(\sin x/x)^4dx=\pi/3$}
The <triangular function> $f(x)=(1-|x|)$ on $|x|<1$, zero elsewhere, has <Fourier transform> $\widehat f(k)=[\sin(k/2)/(k/2)]^2$ in the angular-frequency convention. Its squared <L2 norm> is $2/3$. <Parseval's identity> therefore gives
$$
\frac23=\frac1{2\pi}\int_{-\infty}^{\infty}\left(\frac{\sin(k/2)}{k/2}\right)^4dk=\frac2\pi\int_0^\infty\left(\frac{\sin u}u\right)^4du.
$$
This proves the displayed value. The removable value at zero is one, and the fourth-power decay bounds the tail. The <sinc-squared integral> follows similarly from a rectangular function rather than a triangle.
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