$Si{n}^2{27}^0 + Si{n}^2{87}^0 + Si{n}^2{33}^0 =$

$\begin{array}{rcl} & & {\mathrm{Sin}}^2{27}^0 + {\mathrm{Sin}}^2{87}^0 + {\mathrm{Sin}}^2{33}^0\\ & =& 1-{\cos }^2{87}^0+{\sin }^2{27}^0+\frac{1-\cos 2\left({33}^0\right)}{2}\\ & =& 1-\left({\cos }^2{87}^0-{\sin }^2{27}^0\right)+\frac{1}{2}-\frac{1}{2} \cos {66}^0\\ & =& 1-\cos {114}^0 \cos {60}^0+\frac{1}{2}-\frac{1}{2} \cos {66}^0\\ & =& 1-\cos \left({180}^0-{66}^0\right) \frac{1}{2}+\frac{1}{2}-\frac{1}{2} \cos {66}^0\\ & =& 1+\frac{1}{2}+\frac{1}{2} \cos {66}^0-\frac{1}{2} \cos {66}^0\\ & =& \frac{3}{2}\end{array}$