I found the next problem in a plane geometry book I have been reading.
If two intersecting lines $a_1x+b_1y+c_1=0$ and $a_2x+b_2y + c_2=0$ make an angle $\alpha$ at the intersection, show that
$\sin\alpha=\frac{a_2b_1-a_1b_2}{\sqrt{a_1^2+b_1^2}\sqrt{a_2^2+b_2^2}}$
I have tried using the fact that $\sin\theta= ±\frac{\tan\theta}{\sqrt{1+\tan^2\theta}}$ but I can't conclude what the exercise says.