PE-MO 2016

Let $ABCD$ be a trapezoid of parallel bases $BC$ and $AD$ . If $\angle CAD = 2\angle CAB, BC = CD$ and $AC = AD$ , determine all the possible values of the measure of the angle $\angle CAB$ .

How many dominoes can be placed on a at least $3 \times 12$ board, such so that it is impossible to place a $1\times 3$ , $3 \times 1$ , or $2 \times 2$ tile on what remains of the board?

Clarification: Each domino covers exactly two squares on the board. The chips cannot overlap.