Troubling Trigono

Geometry Level 3

Given that

\[ \sin \theta + \sin^2 \theta + \sin^3 \theta = 1, \]

find the value of

\[ \cos^6 \theta - 4 \cos^4 \theta + 8 \cos ^2 \theta \]

Please share your solution. I am really confused about this problem.

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