Answer
$2\sqrt {3}+1$
Work Step by Step
RECALL:
(1) $\cot{\theta}=\dfrac{\cos{\theta}}{\sin{\theta}}$
(2) $\csc{\theta}=\dfrac{1}{\sin{\theta}}$
With $\sin{\frac{\pi}{3}}=\frac{\sqrt3}{2}$ and $\cos{\frac{\pi}{4}}=\sin{\frac{\pi}{4}}=\frac{\sqrt2}{2}$, then
$3\csc\dfrac {\pi}{3}+\cot \dfrac {\pi }{4}
\\=3\times \left(\dfrac {1}{\sin \dfrac {\pi }{3}}\right)+\dfrac {\cos \dfrac {\pi }{4}}{\sin \dfrac {\pi }{4}}
\\=3\times \left(\dfrac {1}{\dfrac {\sqrt {3}}{2}}\right)+\dfrac {\dfrac {\sqrt {2}}{2}}{\dfrac {\sqrt {2}}{2}}
\\=(3 \times \frac{2}{\sqrt3})+1
\\=2\sqrt {3}+1$
