Can I trisect your angle?Geometry Level 4
In \(\triangle ABC\), \(AB=4\) and \(\angle B=45^\circ\). Cevians \(BD\) and \(BE\) (\(D, E \in AC\)) divide \(\angle B\) into three congruent angles. If \(BD\) is a median of \(\triangle ABC\), find \(BD^2\).
A cevian is a segment from one vertex of the triangle to the opposite side.