8.3. As shown in Figure 1, let quadrilateral $ABCD$ be a rhombus, with points $E$ and $F$ located on sides $AB$ and $BC$, respectively, and $AE = 5BE$, $BF = 5CF$. If $\triangle DEF$ is an equilateral triangle, find the measure of $\angle BAD$.
8.3. As shown in Figure 6, from the problem, we know that $B E = C F$. Take a point $K$ on side $A B$ such that $A K = B E$. It is easy to see that $\triangle A K D \cong \triangle C F D$. Therefore, $D K = D F = D E$. Hence, $\triangle D K E$ is an isosceles triangle, so $\angle D K E = \angle D E K$.
Also, $A K = B E, D K = D E, \angle D K A = \angle D E B$, then $\triangle A D K \cong \triangle B D E$. Therefore, $A D = B D$, thus, $\triangle A B D$ is an equilateral triangle. Therefore, $\angle B A D = 60^{\circ}$.