Task 1. Solve the equation $2|x-1| \sin x=x-1$.

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Answer. $1 ; \frac{\pi}{6}+2 \pi n, n=1,2, \ldots ;-\frac{\pi}{6}+2 \pi n, n=0,-1,-2, \ldots ; \pm\left(\frac{5 \pi}{6}+2 \pi n\right), n=0,1,2, \ldots$.