Sum, Difference, and Multiple-Angle Formulas · Superchallenge problem

A sequence has $a_1 = 2$ and $a_{n+1} = \dfrac{a_n + \sqrt{3}}{1 - \sqrt{3}\,a_n}$ for $n \ge 1$. Find $a_1 + a_2 + a_3 + \cdots + a_{30}$.