The value of the limit
$$\lim_{x \rightarrow {\frac{\pi}{2}}}\frac{4\sqrt{2}(\sin 3x + \sin x)}{\left(2 \sin 2x \sin \frac{3x}{2} + \cos \frac{5x}{2} \right) - \left(\sqrt{2} + \sqrt{2} \cos 2x + \cos \frac{3x}{2}\right)}$$
is_________.
Correct Answer: e
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