$\frac{\mathrm{tg}{23}^o\cdot \mathrm{tg}{67}^o-2}{{\sin }^2{17}^o+{\sin }^{2}73}=\frac{\frac{1}{\mathrm{tg}\left({90}^o-{23}^o\right)}\cdot \mathrm{tg}{67}^o-2}{{\sin }^2{17}^o+{\sin }^2\left({90}^o-{17}^o\right)}=\frac{\frac{1}{\mathrm{tg}{67}^o}\cdot \mathrm{tg}{67}^o-2}{{\sin }^2{17}^o+{\cos }^{2}17}=\frac{1-2}{1}=-1$