What is the exact value of $sin (2 sin^{- 1} (0.6))$ ?

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What is the exact value of $tan (2 tan^{- 1} (\frac{1}{5}) - \frac{π}{4})$ ?
How many solutions does the trigonometric equation $sin^{2} x - 3 sin x + 2 = 0$ have in the closed interval $[0, 2 π]$ ?
What is the principal value of $sin^{- 1} (sin \frac{5 π}{3})$ ?
What is the exact value of $cos (\frac{1}{2} cos^{- 1} (\frac{1}{8}))$ ?
What is the natural domain of the real-valued function $f (x) = sin^{- 1} (2 x - 1)$ ?
What is the exact product $cos 2 0^{\circ} cos 4 0^{\circ} cos 8 0^{\circ}$ ?