$\frac{\mathrm{Tan}{225}^{\circ }-\mathrm{Cot}{81}^{\circ }.\mathrm{Cot}{69}^{\circ }}{\mathrm{Cot}{261}^{\circ }+\mathrm{Tan}{21}^{\circ }}=$

$\begin{array}{rcl} & & \frac{\mathrm{Tan}{225}^{\circ }-\mathrm{Cot}{81}^{\circ }.\mathrm{Cot}{69}^{\circ }}{\mathrm{Cot}{261}^{\circ }+\mathrm{Tan}{21}^{\circ }}\\ & =& \frac{1-\cot {81}^{\circ } \cot {69}^{\circ }}{\cot ({180}^{\circ }+{81}^{\circ })+\tan ({90}^{\circ }-{69}^{\circ })}\\ & =& \frac{-(\cot {81}^{\circ } \cot {69}^{\circ }-1)}{\cot {81}^{\circ }+\cot {69}^0}\\ & =& -\cot ({81}^{\circ }+{69}^{\circ })\\ & =& -\mathrm{coy}{150}^{\circ }\\ & =& \sqrt{3}\end{array}$