If $\alpha \leq 2 \sin^{-1} x + \cos^{-1} x \leq \beta$, then
$\alpha = -\frac{\pi}{2}, \beta = \frac{\pi}{2}$
$\alpha = -\frac{\pi}{2}, \beta = \frac{3\pi}{2}$
$\alpha = 0, \beta = \pi$
$\alpha = 0, \beta = 2\pi$
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