Let \( \mathrm{p} \& \mathrm{q} \) are real numbers such that \( (\tan p-1)^{3}+2019 \) \( (\tan...

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Let \( \mathrm{p} \& \mathrm{q} \) are real numbers such that \( (\tan p-1)^{3}+2019 \) \( (\tan p-1)=-1 \&(1-\cot q)^{3}+2019(1-\cot q)=-1 \tan p \neq \) \( \cot q \), then number of possible values of \( \mathrm{r} \) which satisfy the equation \( \tan p+\cot q+\sin r+\cos r=3 \) in \( r \in[-2 \pi, 2 \pi] \) is
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