If \( 2^{2 \pi / \sin ^{-1} x}-2(a+2) 2^{\pi / \sin ^{-1} x}+8 a0 \) for at least one real \( x ...
If \( 2^{2 \pi / \sin ^{-1} x}-2(a+2) 2^{\pi / \sin ^{-1} x}+8 a0 \) for at least one real \( x \), then
(1) \( \frac{1}{8} \leq a2 \)
(2) \( a2 \)
(3) \( a \in R-\{2\} \)
(4) \( a \in\left[0, \frac{1}{8}\right) \cup(2, \infty) \)
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