# Don't Guess

Algebra Level 4

\begin{align} A&=\left \{z: \arg (z)=\frac{\pi}3 \right \}\\ B&=\left \{z: \arg \left(z-2-2\sqrt 3i \right)=\frac{2\pi}3 \right \} \end{align}

$$A$$ and $$B$$ are two sets defined as shown above.

Find the number of elements in $$A\cap B$$.

Notation: The function $$\arg (z)$$ denotes the argument of a complex number.

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