\[\large \displaystyle \lim_{x \to 0} \dfrac{\sin x^4 - x^4 \cos x^4 + x^{20}}{x^4 \left( e^{2{x}^{4}} - 2 x^4 - 1 \right)} ~ = ~ ?\]

Submit your answer rounded up to 3 places of decimal.

**Notation:** \(e \approx 2.71828\) is the Euler's number.

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