a) Determine if there exists a convex hexagon $ABCDEF$ with $$\angle ABD + \angle AED > 180^{\circ},$$$$\angle BCE + \angle BFE > 180^{\circ},$$$$\angle CDF + \angle CAF > 180^{\circ}.$$b) The same question, with additional condition, that diagonals $AD, BE,$ and $CF$ are concurrent.