We know the very well-known identity:
$$\sum_{n=-\infty}^\infty\text{sinc}(n)=\pi.$$
But how to show that
$$\sum_{n=-\infty}^\infty\text{sinc}(x+n)=\pi?$$
In other words, how to prove that
$$\sum_{n=-\infty}^\infty\text{sinc}(x)=\pi, \qquad \forall x?$$
Any ideas?