Consider the following '(pseudo)function':
$$g(x)= \frac{\sin^2\pi x}{(\pi x)^2\left(1-x^2\right)^2} \prod_{n=2}^\infty \frac{\pi x}{n\sin\frac{\pi x}{n}}$$
Now consider the following products :
$$\prod_{k=2}^c (\frac{1}{1+\frac{k}{g(k)}} + \frac{1}{1+\frac{2c-k}{g(2c-k)}})$$
Or
$$\prod_{k=2}^c (\frac{1}{1+\frac{1}{g(k)}} + \frac{1}{1+\frac{1}{g(2c-k)}})$$
What are some possible (workable) Rearrangments of the above products ?
Note : Not a trivial function ; could have application to Goldbach Conjecture .