Question: Consider (f(x)=4 sin ^{3} 2 x). a. Derive the trigonometric identity giving (sin ^{3} theta) in terms of (sin theta) and (sin 3 theta) using

Consider \(f(x)=4 \sin ^{3} 2 x\).

a. Derive the trigonometric identity giving \(\sin ^{3} \theta\) in terms of \(\sin \theta\) and \(\sin 3 \theta\) using DeMoivre's Formula.

b. Find the Fourier series of \(f(x)=4 \sin ^{3} 2 x\) on \([0,2 \pi]\) without computing any integrals.

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