For some complex number $\omega$ with $|\omega| = 2016$, there is some real $\lambda>1$ such that $\omega$, $\omega^{2}$, and $\lambda \omega$ form an equilateral triangle in the complex plane. Then, $\lambda$ can be written in the form $\frac{a + \sqrt{b}}{c}$, where $a,b,$ and $c$ are positive integers and $b$ is squarefree. Compute $\sqrt{a+b+c}$.

Let's think step by step and output the final answer within \boxed{}.
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