Question 27Suppose $a$ 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 $\dfrac1{a^2}+\dfrac1{b^2}+\dfrac1{c^2}+\dfrac1{d^2}$.