What is the exact value of $tan (2 tan^{- 1} (\frac{1}{5}) - \frac{π}{4})$ ?

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How many solutions does the trigonometric equation $sin^{2} x - 3 sin x + 2 = 0$ have in the closed interval $[0, 2 π]$ ?
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What is the natural domain of the real-valued function $f (x) = sin^{- 1} (2 x - 1)$ ?
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