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Let $K$ be the set of all real values of $x$ where the function $f(x) = \sin|x| - |x| + 2(x - \pi)\cos|x|$ is not differentiable. Then the set $K$ is equal to:
(1) $\phi$ (an empty set)
(2) ${\pi}$
(3) ${0}$
(4) ${0, \pi}$
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