Find the fraction of the interval $0 \leq \theta \leq \pi$ for which the inequality $$\left(\sin(2\theta) - \frac{1}{2}\right)(\sin\theta - \cos\theta) \geq 0$$ is satisfied.
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Find the fraction of the interval $0 \leq \theta \leq \pi$ for which the inequality
$$\left(\sin(2\theta) - \frac{1}{2}\right)(\sin\theta - \cos\theta) \geq 0$$
is satisfied.