If `sintheta+sin^2theta+sin^3theta=1,` then prove that `cos^6theta-4cos^4theta+8cos^2theta=4`

Explanation

To prove that \( \cos^6 \theta - 4 \cos^4 \theta + 8 \cos^2 \theta = 4 \) given that \( \sin \theta + \sin^2 \theta + \sin^3 \theta = 1 \), we will follow these steps:

### Step 1: Rewrite the equation in terms of \( \sin \theta \)

Given:
\[ \sin \theta + \sin^2 \theta + \sin^3 \theta = 1 \]
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