\[\cos\theta + \cos^{2}\theta + \cos^{3}\theta = 1\]

Given the above trigonometric equation. And if the trigonometric equation below is also true for constants \(a,b,c\). Find the value of \(a+b+c\).

\[ \sin^{6}\theta = a + b\sin^{2}\theta + c\sin^{4}\theta\]

This problem is part of the set Trigonometry.

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