Trigo trouble

Geometry Level 3

$\sqrt[3]{\sec\frac{2\pi }{7}} + \sqrt[3]{\sec\frac{4\pi }{7}} + \sqrt[3]{\sec\frac{8\pi }{7}} = \sqrt[3]{a-b\sqrt[3]{c}}$

Where $$a$$, $$b$$ and $$c$$ are integers, then $$a+b+c =$$

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