Trisect Side of Equilateral Triangle

Geometry Level 3

In an equilateral $$\triangle ABC$$, the side $$BC$$ is trisected at $$D$$ with $$BD= \frac{1}3 BC$$. The value of $$\dfrac{AD^2}{AB^2}$$ can be expressed as $$\dfrac{m}n$$, where $$m$$ and $$n$$ are coprime positive integers. Find $$m+n$$.

×