The total number of solutions of \( |\cot x|=\cot x+\frac{1}{\sin x} \), \( \mathrm{P} \) \( x \...

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The total number of solutions of \( |\cot x|=\cot x+\frac{1}{\sin x} \),
\( \mathrm{P} \) \( x \in[0,3 \pi] \), is equal to

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(1) 1
(2) 2
(3) 3
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