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Use the definition of a Taylor series to find the first four nonzero terms of the series for $ f(x) $ centered at the given value of $ a. $

$ f(x) = \sin x, $ $ a = \pi/6 $

$$\frac{1}{2}+\frac{\sqrt{3}}{2}\left(x-\frac{\pi}{6}\right)-\frac{1}{4}\left(x-\frac{\pi}{6}\right)^{2}-\frac{\sqrt{3}}{12}\left(x-\frac{\pi}{6}\right)^{3}$$

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