What is \(6\sin(\pi/18) - 8\sin^3(\pi/18)\) equal to?
\(1\)
Using the triple angle identity \(\sin3\theta = 3\sin\theta-4\sin^3\theta\) with \(\theta=\pi/18\) (that is, \(10°\)), \(6\sin\theta-8\sin^3\theta=2(3\sin\theta-4\sin^3\theta)=2\sin3\theta=2\sin30°=2\times\dfrac{1}{2}=1\).
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