Coming back home after a few strikes

From one corner A of a fixed regular billiards table ABCD placed on a horizontal surface. A ball of mass m=2kg and negligible dimensions is projected in the horizontal plane. The coefficient of restitution is 0.5 for every collision. It strikes the sides in order BC , AD , DC ,BC , and then returns to the same point A then the angle of initial projection it makes with side AB is \( \theta \)

If the ratio of sides AB:BC is 5:1, find \( \lfloor 100tan\theta \rfloor \).

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