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]