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Let $$P = \left\{\theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta\right\}$$ and $$Q = \left\{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta\right\}$$ be two sets. Then
$$P \subset Q$$ and $$Q - P \neq \varnothing$$
$$Q \not \subset P$$
$$P \not \subset Q$$
$$P = Q$$
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