Sin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6)

The given expression is $\sin \frac{\pi}{3} \cos \frac{\pi}{6} + \cos \frac{\pi}{3} \sin \frac{\pi}{6}$. This matches the sine addition formula:

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

In this problem, $A = \frac{\pi}{3}$ and $B = \frac{\pi}{6}$.
Substitute these values into the formula:

$$\sin\left(\frac{\pi}{3} + \frac{\pi}{6}\right)$$

To add the fractions, find a common denominator:

$$\frac{\pi}{3} + \frac{\pi}{6} = \frac{2\pi}{6} + \frac{\pi}{6} = \frac{3\pi}{6} = \frac{\pi}{2}$$

We know that $\sin \frac{\pi}{2}$ is a standard trigonometric value:

$$\sin \frac{\pi}{2} = 1$$

The final value is:

$$\sin \frac{\pi}{3} \cos \frac{\pi}{6} + \cos \frac{\pi}{3} \sin \frac{\pi}{6} = \boxed{1}$$