27. Suppose $a$ and $b$ are the roots of $x^{2}+x \sin \alpha+1=0$ while $c$ and $d$ are the roots of the equation $x^{2}+x \cos \alpha-1=0$. Find the value of $\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}+\frac{1}{d^{2}}$.