\((\text{i})\) By first writing \(\sin 3 \theta\) as \(\sin (2 \theta + \theta)\), show that \[\sin 3 \theta = 3 \sin \theta - 4 \sin^3 \theta . \]

\((\text{ii})\) Determine the greatest possible value of \[9 \sin \left (\dfrac{10}{3} \alpha \right )- 12 \sin^3 \left (\dfrac{10}{3} \alpha \right )\] and find the smallest positive value of \(\alpha\) (in degrees) for which that value occurs.

\((\text{iii})\) Solve, for \(0°< \beta < 90°\), the equation \( 3 \sin 6 \beta \, \text{csc} \, 2 \beta = 4\). Give your answer(s) to 3 significant figures.

**Input the largest possible value of \( \beta\) as your answer.**

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