# Sine of a product

Calculus Level 5

$\sin \left( \displaystyle \prod_{n=1}^{\infty} \left[ \dfrac{(2n)^2}{(2n-1)(2n+1)}\right] \right) = \mathfrak{K}$

Find $$\left \lfloor 10^3 \mathfrak{K} \right \rfloor$$.

Details and assumptions:

• The argument of sine is given in radians.
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