\[ \lim_{x \to 0} \frac{\cos^3(x) - 1}{\cos^3(x) + \cos(x) - 2} = \frac{\cos^3(0) - 1}{\cos^3(0) + \cos(0) - 2} = \frac{1 - 1}{1 + 1 - 2} = 0 \]
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