Interpreting congruent angles!

$\large{ Q= \dfrac{\left(\dfrac{1}{|BA_1|} + \dfrac{1}{|BA_{n+1}|} \right)}{\left( \dfrac{1}{|BA_1|} + \dfrac{1}{|BA_2|} + \ldots + \dfrac{1}{|BA_n|} + \dfrac{1}{|BA_{n+1}|} \right)} }$

Given an $\angle ABC = \phi$ and rays $l_1, l_2, \ldots, l_{n-1}$ dividing the angle into $n$ congruent angles. For a line $l$ intersecting sides $AB$ and $BC$ at two distinct points, denote $l \cap (AB) = A_{1}$ , $l \cap (BC) = A_{n+1}$ and $l \cap l_i = A_{i+1}$ for $1 \leq i < n$ . Show that the value of $Q$ is a constant which doesn't depend on $l$ , and find the value of $Q$ in terms of $n$ and $\phi$ .

If $n=5, \ \phi = 75^\circ$ , then $Q$ can be expressed as $\large{A - \dfrac{B}{\sqrt{C}}},$

where $A,B$ and $C$ are positive integers, and $C$ square-free, find the value of $A+B+C$ .