I was intrigued by this answer the other day, but perhaps lack a little bit of the necessary background to understand a certain step.
Namely, the fact that $$\prod_{n=1}^{+\infty} \left(\frac{\sin\left(\frac{\pi}{6\cdot 2^{n-1}}\right)}{2\sin\left(\frac{\pi}{6\cdot 2^n}\right)}\right)^2 = \left(\frac{3}{\pi}\right)^{2}$$ is used, and I cannot make sense of this at all. Jack D'Aurizio comments that "the product of squares is the square of the product" but I'm not entirely sure what this means. Can anyone explain it to me a little more in-depth? I'm not sure what to look up to understand this foreign concept.
Edit: With a hint from Simon S I got the answer, so I have to thank him very much. I'm not sure what to do with my question now.