I am trying to express $\tan(x)$ as an infinite product. So far I have found 4 factors $$x\frac{(\frac{x^2-\pi^2}{\pi^2})(\frac{x^2-4\pi^2}{1})(\frac{x^2-9\pi^2}{1})(\frac{x^2-16\pi^2}{1})}{1.33554327...(x^2-\frac{\pi^2}{4})(x^2-\frac{9\pi^2}{4})(x^2-\frac{25\pi^2}{4})(x^2-\frac{49\pi^2}{4})}$$
As you can see, I have accounted for the zeroes at $0$, $\pi$, $2\pi$.. and asymptotes at $\frac{\pi}{2}$...$\space$ However when I try to scale it down with more than 2 $\pi$'s as shown above, I see that the function becomes too curved and does not match up, it only seems to line up when I divide by another number $1.33554327...$. I am unsure as to where this number comes from and I would like to know why dividing by $\pi$, $2\pi$.. does not help match the function with $\tan(x)$ and how to scale the product (what should I divide the top factors by?)