<s>[INST] Finding the value of $\sin {\frac{31 \pi}3}$ The task was to find out the value of $$\sin\frac{31\pi}3$$
This is a example in my book in which following steps are shown:
$$\begin{align}
\sin\frac{31\pi}3& =\sin\left(10\pi +\frac\pi3\right)\\
&=\sin\frac\pi3\\
&=\frac{\sqrt3}2
\end{align}$$
I cannot understand step 3, $=\sin\frac\pi3$
 [/INST] You can confirm this by using the angle-sum formula:
$$\begin{align} \sin(10\pi + \pi/3) & = \sin(10\pi)\cos(\pi/3) + \cos(10 \pi)\sin(\pi/3) \\ \\ & = 0\cdot\frac 12 + 1 \cdot \sin (\pi/3) \\ \\ & = \sin(\pi/3)\\ \\ & = \sqrt 3/2\end{align}$$
</s>