There exist constants $a$ and $b$ so that
\[\cos^3 \theta = a \cos 3 \theta  + b \cos \theta\]for all angles $\theta.$  Enter the ordered pair $(a,b).$
Question:
There exist constants $a$ and $b$ so that
\[\cos^3 \theta = a \cos 3 \theta  + b \cos \theta\]for all angles $\theta.$  Enter the ordered pair $(a,b).$
Answer:
Let's think step by step.

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\left( \frac{1}{4}, \frac{3}{4} \right)
There exist constants $a$ and $b$ so that
\[\cos^3 \theta = a \cos 3 \theta  + b \cos \theta\]for all angles $\theta.$  Enter the ordered pair $(a,b).$
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