Figure 3 shows a sketch of part of the curve with parametric equations $$\[ x=\tan \theta \quad y=2 \sin 2 \theta \quad \theta \geqslant 0 \]$$ The finite region, shown shaded in Figure 3, is bounded by the curve, the $$\(x\)$$-axis and the line with equation $$\(x=\sqrt{3}\)$$ The region is rotated through $$\(2 \pi\)$$ radians about the $$\(x\)$$-axis to form a solid of revolution. (a) Show that the exact volume of this solid of revolution is given by $$\[ \int_{0}^{k} p(1-\cos 2 \theta) d \theta \]$$ where $$\(p\)$$ and $$\(k\)$$ are constants to be found. (7) (b) Hence find, by algebraic integration, the exact volume of this solid of revolution. (3)

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