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$\lim _{x \rightarrow \pi / 6} \frac{\cot ^2 \theta-3}{\operatorname{cose} \theta-2}=$
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$4$
$\lim _{x \rightarrow \pi / 6} \frac{\operatorname{cosec}^2 \theta-4}{\operatorname{cosec} \theta-2}=\lim _{x \rightarrow \pi / 6} \operatorname{cosec} \theta+2=4$ \(\left( \text{as, }1+\cot ^2 \theta=\operatorname{cosec}^2 \theta\right)\)
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