Exercises: Symmetry and Periodicity of Trigonometric Functions

A point travels counterclockwise around the unit circle.
After one complete revolution (adding $2\pi$ radians to the angle),
the terminal point returns to its starting position.

If $\sin\!\left(\dfrac{\pi}{6}\right) = \dfrac{1}{2}$,
what is $\sin\!\left(\dfrac{\pi}{6} + 2\pi\right)$?

Enter your answer as a fraction.