Sea $ABCDEF$ un hexágono convexo tal que $\angle B+\angle D+\angle F=360^{\circ }$ y\n\[ \frac{AB}{BC} \cdot \frac{CD}{DE} \cdot \frac{EF}{FA} = 1. \]\nDemostrar que\n\[ \frac{BC}{CA} \cdot \frac{AE}{EF} \cdot \frac{FD}{DB} = 1. \]