End-of-the-year complex recurrence problem

Algebra Level 5

\[2a_n=(1-\mathrm{i}\sqrt{3}-2\mathrm{i})a_{n-1}+(\sqrt{3}+\mathrm{i})a_{n-2}\]

\[a_0=0, a_1=1-\mathrm{i}\sqrt{3}+2\mathrm{i}\]

\(|a_{2015}|^2\) can be written as \(r - s\sqrt{t}\), where \(r\) and \(s\) are positive integers and \(t\) is a square-free positive integer. What is \(r + s + t\)?

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