A siny limit

Calculus Level 4

\[\large \lim_{x\to 1}\left( \frac{-ax+\sin(x-1)+a}{x+\sin(x-1)-1} \right)^{\frac{1-x}{1-\sqrt{x}}} = \frac{1}{4}\]

Find the value of the non-zero constant \(a\) satisfying the equation above.

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