When is $\sin x$ or $\sin 2x$ larger than a half?

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The fraction of the interval \(0\leq x \leq 2\pi\), for which one (or both) of the inequalities \[\sin x \geq\frac{1}{2}, \qquad \sin 2x \geq \frac{1}{2}\] is true, equals

1. \(\dfrac{1}{3}\);

2. \(\dfrac{13}{24}\);

3. \(\dfrac{7}{12}\);

4. \(\dfrac{5}{8}\).