The value of $cot\frac{\pi }{24} is :$

$\begin{array}{rcl} & & \cot \frac{\mathrm{\pi }}{24}\\ \cot \mathrm{A}& =& \tan \mathrm{A}+2\cot 2\mathrm{A}\\ \cot \mathrm{A}& =& -\tan \mathrm{A}+2\mathrm{cosec}2\mathrm{A}\\ \cot \mathrm{A}& =& \cot 2\mathrm{A}+\mathrm{cosec}2\mathrm{A}\\ \cot \frac{\mathrm{\pi }}{24}& =& \cot \frac{\mathrm{\pi }}{12}+\mathrm{cosec}\frac{\mathrm{\pi }}{12}\\ & =& 2+\sqrt{3}+\sqrt{2} \left(\sqrt{3}+1\right)\\ & =& 2+\sqrt{3}+\sqrt{6}+\sqrt{2}\end{array}$