A limaçon is a graph of a polar equation $r=a+b\cos(\theta)$ or $r=a+b\sin(\theta)$ where $a<b$. It is a smooth curve that looks like a loop that twists to have a loop in the middle as well. How can you know the values of the start and end of the inner loop?
The loop starts and ends at the origin, so you are looking for the points where $r=0$. That is, $$\tag1 a+b\cos t=0, $$ or $$\tag2 \cos t=-\frac ab. $$ As the cosine takes each value twice, there will be two solutions to $(2)$, that will give you the two values where the curve enters and exits the loop.