Can we find the area between $\sin x$ and $\sin 2x$?

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Using the same axes, sketch the curves \(y = \sin x\) and \(y = \sin 2x\) from \(x = 0\) to \(\tfrac{1}{2}\pi\), where \(x\) is in radians.

Prove that the curves intersect at the points \[ (0,0) \quad\text{and}\quad \left(\frac{\pi}{3}, \frac{\sqrt{3}}{2} \right). \]

Calculate the area of the region bounded by the parts of the curves between these two points.