Trigonometry (7)

If $\displaystyle\prod_{r=1}^{\infty}\cos\left(\frac{x}{2^{r}}\right)=\frac{\sin x}{x}$ then find the value of $\displaystyle\sum_{r=1}^{\infty}\frac{1}{2^{2r}}\sec^{2}\left(\frac{x}{2^{r}}\right)$ at $x=\frac{\pi}{2}$

If your answer is in the form of $a-\frac{b}{\pi^{c}}$ , where $a,b,c$ are rational numbers, then find the value of $\log_{c}(ab)$ .

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