How to prove $ \sin x=...(1+\frac{x}{3\pi})(1+\frac{x}{2\pi})(1+\frac{x}{\pi})x(1-\frac{x}{3\pi})(1-\frac{x}{2\pi})(1-\frac{x}{\pi})...$? [duplicate]

trigonometry

Courtesy of Edmund Landau, from his Differential and Integral Calculus.

enter image description hereenter image description hereenter image description hereenter image description here

enter image description here

Related

How to describe all normal subgroups of the dihedral group Dn? [duplicate]
Proving that : $ \left|\int_a^b\frac{\widehat{f}(\xi)}{\xi}d\xi\right|\le 4 \|f\|_1$ for all $a,b$ and all $f$
Prove by induction: $\sum\limits_{k=1}^{n}sin(kx)=\frac{sin(\frac{n+1}{2}x)sin\frac{nx}{2}}{sin\frac{x}{2}}$
Period of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$
Number of binary strings of length 8 that contain either three consecutive 0s or four consecutive 1s
Identifying 2 poisoned wines out of 2^n wines
Counting heptagons formed using vertices of $n$-sided polygon having no sides in common with the polygon
Show convergence of recursive sequence and find limit value
Examples of Lie algebras of the $BC$ root system type
Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$
Coloring a cube with 4 colors
Topology: Proof that a finitely generated cone is closed