9709 P3 - Jun 2004 - Q5
1722
(i) Prove the identity \(\sin^2 \theta \cos^2 \theta \equiv \frac{1}{8}(1 - \cos 4\theta)\).
(ii) Hence find the exact value of \(\int_{0}^{\frac{1}{3}\pi} \sin^2 \theta \cos^2 \theta \, d\theta\).
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