MathNet 2023-part-03 — 191 problems (EN–VI) Question 102

We have an equilateral triangle $ABC$ with side length $3$, and points $D$, $E$, and $F$ on sides $BC$, $CA$, and $AB$, respectively. Given that $BD = 1$ and $\angle ADE = \angle DEF = 60^\circ$, find the length of segment $AF$.