Let \( S=\left\{t \in R: f(x)=|x-\pi| .\left(e^{|x|}-1\right) \sin ...

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Let \( S=\left\{t \in R: f(x)=|x-\pi| .\left(e^{|x|}-1\right) \sin |x|\right. \) is not differentiable at t. \( \} \) Then the set \( S \) is equal to :
(1) \( \{\pi\} \)
(2) \( \{0, \pi\} \)
(3) \( \phi \) (an empty set)
(4) \( \{0\} \)
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