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Given that 0∘≤θ≤360∘0^{\circ}\leq\theta\leq 360^{\circ}0∘≤θ≤360∘ satisfies the trigonometric equation
5sinθcos2θ+2cosθ=0,5\sin\theta\cos^2\theta+2\cos\theta=0,5sinθcos2θ+2cosθ=0,
find the number of values θ\thetaθ can take.
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