Answer
$3-3\frac{\sqrt2}{2}$.
Work Step by Step
$\tan{\frac{\pi}{4}}-3\cos{\frac{\pi}{6}}+\csc{\frac{\pi}{6}}=1-3\frac{\sqrt2}{2}+2=3-3\frac{\sqrt2}{2}$.
$\csc{\frac{\pi}{6}}=\dfrac{1}{\sin{\frac{\pi}{6}}}=\dfrac{1}{\frac{1}{2}}=2.$
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