Answer
$1+2\sqrt 3$
Work Step by Step
Note that $\csc x=\dfrac{1}{\sin x}$ and $\cot x=\dfrac{1}{\tan x}$
We use the unit circle values to simplify.
Since $\sin{\frac{\pi}{3}}=\frac{\sqrt3}{2}$ and $\tan{\frac{\pi}{4}}=1$, then
$3 \ \csc \frac{\pi}{3} + \cot \frac{\pi}{4}\\
=3 \cdot \dfrac{1}{\sin{\frac{\pi}{3}}} + \dfrac{1}{\tan{\frac{\pi}{4}}}\\
= \dfrac{3}{\frac{\sqrt3}{2}} + \dfrac{1}{1} \\
=3\cdot \frac{2}{\sqrt3} + 1 \\
=\frac{6}{\sqrt3}+1\\
=\frac{6\sqrt3}{3}+1\\
=2\sqrt3+1\\
=1+2\sqrt3$
