As for your equation, just by looking at it I'm guessing that it's an infinite product approximation of something that roughly behaves like sinc(x) = sin(x)/x, and is also shifted by Pi/2 on the x-axis.
it has the property
f(x) f(-x) = \frac{\sin x}{x}
So I wasn't too far off... Interesting property. Does the equation have any practical application, say, in digital filtering, sampling or similar? Or was it constructed just for the lulz?
... it has applications in number theory (maybe breaking some crypto?), I like how you've taken a shine to it!
... now if you could just expand as an infinite sum and let me know if you find a close-formed expression for the 3rd term (or higher) coefficients, that would be great, thanx. I'll likely offer a btc bounty for the correct solution for this someday but will definitely make you co-author on a paper to make you famous anyway.