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7.1.3. Find the greatest negative root of the equation

$$\frac{\sin \pi x - \cos 2 \pi x}{(\sin \pi x + 1)^2 + \cos^2 \pi x} = 0.$$

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Official solution

Answer: $-\frac{7}{6} \approx-1.17$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.