Four real constants \( a, b, A, B \) are given and \( f(\theta)=1-a \cos \theta-b \sin \theta-A ...

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Four real constants \( a, b, A, B \) are given and \( f(\theta)=1-a \cos \theta-b \sin \theta-A \cos 2 \theta-B \sin 2 \theta \). Prove that if \( f(\theta) \geq 0, \forall \theta \in R \), then \( a^{2}+b^{2} \leq 2 \) and \( A^{2}+B^{2} \leq 1 \).
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