Triple Cosine to Triple Sine

Geometry Level 4

$\cos\theta + \cos^{2}\theta + \cos^{3}\theta = 1$

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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