Four real constants aaa, bbb, AAA, BBB are given, and f(θ)=1−acosθ−bsinθ−Acos2θ−Bsin2θ.f(\theta) = 1 - a\cos\theta - b\sin\theta - A\cos 2\theta - B\sin 2\theta.f(θ)=1−acosθ−bsinθ−Acos2θ−Bsin2θ. Prove that if f(θ)≥0f(\theta) \geq 0f(θ)≥0 for all real θ\thetaθ, then a2+b2≤2 and A2+B2≤1.a^2 + b^2 \leq 2 \text{ and } A^2 + B^2 \leq 1.a2+b2≤2 and A2+B2≤1.