$x$ satisfies the simultaneous equations $$\sin 2x + \sqrt{3}\cos 2x = -1$$ and $$\sqrt{3}\sin 2x - \cos 2x = \sqrt{3}$$ where $0^{\circ} \leq x \leq 360^{\circ}$. Find the sum of the possible values of $x$.
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$x$ satisfies the simultaneous equations
$$\sin 2x + \sqrt{3}\cos 2x = -1$$
and
$$\sqrt{3}\sin 2x - \cos 2x = \sqrt{3}$$
where $0^{\circ} \leq x \leq 360^{\circ}$.
Find the sum of the possible values of $x$.