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The set of all possible values of $\theta$ in the interval $(0, \pi)$ for which the points $(1, 2)$ and $(\sin\theta, \cos\theta)$ lie on the same side of the line $x + y = 1$ is:
(1) $\left(0, \frac{\pi}{2}\right)$
(2) $\left(\frac{\pi}{4}, \frac{3\pi}{4}\right)$
(3) $\left(0, \frac{3\pi}{4}\right)$
(4) $\left(0, \frac{\pi}{4}\right)$
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