Let $X = \cos\frac{2\pi}{7} + \cos\frac{4\pi}{7} + \cos\frac{6\pi}{7} + \cdots + \cos\frac{2006\pi}{7} + \cos\frac{2008\pi}{7}$. Compute $\Big|\lfloor 2008 X \rfloor \Big|$.

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