$Si{n}^2{50}^0 + Si{n}^2{70}^0 + Si{n}^2{170}^0=$

$\begin{array}{rcl} & & {\sin }^2{50}^0 + {\sin }^2{70}^0 + {\sin }^2{170}^0\\ & =& 1-{\cos }^2{70}^0+{\sin }^2{50}^0+{\sin }^2({180}^0-{10}^0)\\ & =& 1-\left({\cos }^2{70}^0-{\sin }^2{50}^0+{\sin }^2{10}^0\right)\\ & =& 1-\cos {120}^0 \cos {20}^0+\frac{1-\cos {20}^0}{2}\\ & =& 1+\frac{1}{2}\cos 20+\frac{1}{2}-\frac{1}{2}\cos {20}^0\\ & =& 1+\frac{1}{2}=\frac{3}{2}\end{array}$