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Understanding the Context

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\sin^4 \theta + \cos^4 \theta = (\sin^2 \theta + \cos^2 \theta)^2 - 2\sin^2 \theta \cos^2 \theta = 1 - 2\sin^2 \theta \cos^2 \theta.
Substitute into $ f(\theta) $:
f(\theta) = (1 - 2\sin^2 \theta \cos^2 \theta) - 4\sin^2 \theta \cos^2 \theta = 1 - 6\sin^2 \theta \cos^2 \theta.

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