Given that $\mathrm{cot}\theta =-\sqrt{3}<0\text{}\text{and}\text{}\mathrm{sec}\theta \text{}\text{then}\text{}\theta \text{}\text{is in QII so}\text{}\mathrm{sin}\theta 0$.

since $\mathrm{cot}\theta =-\sqrt{3}=\frac{-\sqrt{3}}{1}\text{}\text{we can let adj}\text{}=\sqrt{3}\text{}\text{and opp}\text{}=1$

$op{p}^{2}+ad{j}^{2}=hy{p}^{2}$

$(1{)}^{2}+(\sqrt{3}{)}^{2}=hy{p}^{2}$$1+3=hy{p}^{2}$

$4=hy{p}^{2}$

$hyp=2$

So, $\mathrm{sin}\theta =\frac{opp}{hyp}$

since $\mathrm{sin}\theta >0$

$\mathrm{sin}\theta =\frac{1}{2}$