2. If the graph of the function $y=2 \sin (2 x+\varphi)$ is symmetric about the point $\left(\frac{2 \pi}{3}, 0\right)$, then the minimum value of $|\varphi|$ is $\qquad$ .
$$
2 \times \frac{2 \pi}{3}+\varphi=k \pi \Rightarrow \varphi=k \pi-\frac{4 \pi}{3} \Rightarrow|\varphi|_{\text {min }}=\frac{\pi}{3} .
$$

Translates to:

$$
2 \times \frac{2 \pi}{3}+\varphi=k \pi \Rightarrow \varphi=k \pi-\frac{4 \pi}{3} \Rightarrow|\varphi|_{\text {min }}=\frac{\pi}{3} .
$$