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)}}=