Prove that \( (2 \sqrt{3}+3) \sin x+2 \sqrt{3} \cos x \) lies between \( -(2 \sqrt{3}+\sqrt{15})...

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Prove that \( (2 \sqrt{3}+3) \sin x+2 \sqrt{3} \cos x \) lies between \( -(2 \sqrt{3}+\sqrt{15}) \) and \( (2 \sqrt{3}+\sqrt{15}) \).
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