Answer
$\sqrt 2$
Work Step by Step
csc($\frac{\pi}{4}$ + 2$\pi$) = csc$\frac{\pi}{4}$
csc$\frac{\pi}{4}$ = $\frac{1}{sin\frac{\pi}{4}}$
csc$\frac{\pi}{4}$ = $\frac{1}{\frac{\sqrt 2}{2}}$ = $\sqrt 2$
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