HMMT 2025 G7

Point $P$ is inside triangle $\triangle A B C$ such that $\angle A B P = \angle A C P$ . Given that $A B = 6$ , $A C = 8$ , $B C = 7$ , and $\frac{B P}{P C} = \frac{1}{2}$ , compute $\frac{|B P C|}{|A B C|}$ .

(Here, $[X Y Z]$ denotes the area of $\triangle X Y Z$ ).