Answer
$-\frac{\pi}{6}$
Work Step by Step
$\frac{\pi}{6}-\frac{\pi}{3}=\frac{\pi}{6}-\frac{\pi\times2}{3\times2}=\frac{\pi}{6}-\frac{2\pi}{6}=\frac{\pi-2\pi}{6}=\frac{-\pi}{6}=-\frac{\pi}{6}$
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