Calculus Level pending

$\Large \displaystyle\int_{0}^{1} \left[ \dfrac{256.i^{6}.\dfrac{d^{2}}{d \theta^{2}} \left \{ \displaystyle\prod_{r=1}^{503} e^{(2r-1)i.\theta} \right \} }{ \displaystyle\prod_{r=0}^{502} e^{(2r+1)i.\theta} } \right]^{\dfrac{1}{4}} d\theta = ?$

Details and Assumptions

• Here $$e$$ is the euler's number.

• Here $$i=\sqrt{-1}$$

• $$\displaystyle{\prod_{n=1}^{k} n}$$ means Continued Product of n upto $$k$$
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