After a night's sleep, I think I found myself a rather simple explanation:
Normally, negative values of r ( = 1-2Cos3t in this case) are not considered in polar coordinates.
However, they indeed seem to not have been discarded here,
but presented in the opposite direction of the pole.
So for instance ( when plotting with limits [0 , 2pi] ) , for t = 4pi/3 , an angle in the
third quadrant, r = -1 , and this value is given as the top of the small loop in the
first quadrant.
No wonder then, that limiting t to [0, 2Pi/3] , no small loop appears in the big one, because inside this latter, r is only negative for values of t outside this region of t.
Another interesting way to see and understand this is asking for r = 1-2Cos3t with limits for t : [-pi/9 , 7pi/9]
