We want to eliminate $r$ and $\theta$ from the equation.
We have $r \cos \left(\theta-\frac{\pi}{6}\right)=2$. Using the angle subtraction formula for cosine, we get:
$$r\left(\cos\theta\cos\frac{\pi}{6} + \sin\theta\sin\frac{\pi}{6}\right) = 2$$
Now, we know
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