Lines $L_1$ ($a_1x+b_1y+c_1$) and $L_2$ ($a_2x+b_2y+c_2$) intersect at a point $P$ and subtend an angle $\theta$ at $P$.
Another line $L$ makes the same angle $\theta$ with $L_1$ at $P$. Find the equation of L.
$$$$All I could think of was to use the concepts of Family of Lines and Angle Bisectors (I couldn't think of how though). We already have the equations of two lines passing through a fixed point $P$. Thus, the equation of $L$ must be of the form $$(a_1x+b_1y+c_1)+\lambda(a_2x+b_2y+c_2)=0$$
However, at this point, I got stuck since I was unable to calculate the value of $\lambda$.
$$$$Any help with this question would be greatly appreciated. Many thanks in anticipation!