Please reason step by step, and put your final answer within \boxed{}.
In $\triangle ABC$, the sides opposite to angles A, B, and C are $a$, $b$, and $c$, respectively. If $$\frac{a^2}{bc} - \frac{c}{b} - \frac{b}{c} = \sqrt{3}$$, and the radius of the circumcircle of $\triangle ABC$ is 3, find $a$.
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