Find the phase shift of the graph of $y =  2 \sin \left( x + \frac{\pi}{3} \right).$
Since the graph of $y = 2 \sin \left( x + \frac{\pi}{3} \right)$ is the same as the graph of $y = 2 \sin x$ shifted $\frac{\pi}{3}$ units to the left, the phase shift is $\boxed{-\frac{\pi}{3}}.$

[asy]import TrigMacros;

size(400);

real g(real x)
{
	return 2*sin(x + pi/3);
}

real f(real x)
{
	return 2*sin(x);
}

draw(graph(g,-3*pi,3*pi,n=700,join=operator ..),red);
draw(graph(f,-3*pi,3*pi,n=700,join=operator ..));
trig_axes(-3*pi,3*pi,-3,3,pi/2,1);
layer();
rm_trig_labels(-5, 5, 2);
[/asy]