Simplify exactly. Be sure that each part of your final answer is in lowest terms with a rational denominator.
−16cos2(60∘)+16sin2(30∘)+12cot2(30∘)=\displaystyle -\frac{{1}}{{6}}{{\cos}^{{2}}{\left({60}^{\circ}\right)}}+\frac{{1}}{{6}}{{\sin}^{{2}}{\left({30}^{\circ}\right)}}+\frac{{1}}{{2}}{{\cot}^{{2}}{\left({30}^{\circ}\right)}}=−61cos2(60∘)+61sin2(30∘)+21cot2(30∘)=
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