Step 1:
We can rewrite the function $f(\theta)$ as follows:
$$
f(\theta)=\sin ^{6} \theta+\cos ^{6} \theta = (\sin^2\theta + \cos^2\theta)^3 - 3\sin^2\theta\cos^2\theta(\sin^2\theta + \cos^2\theta)
$$
Since $\sin^2\theta + \cos^2\theta = 1$, we can simplify this
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