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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