When to use Collections vs when to add extra function to a concrete subclass of a list?

When to use Collections vs when to add extra function to a concrete
subclass of a list?

Consider the following code to detect if linkedlist has a loop
public boolean hasLoop() {
Node<E> fast = first;
Node<E> slow = first;
while (fast != null && fast.next != null) {
fast = fast.next.next;
slow = slow.next;
if (slow == fast) {
return true;
}
}
return false;
}
If Sun Microsystems were to add this functionality into Linkedlist.java,
how would they do it ? Note, Sun uses Node class as an internal detail (ie
private).
A few options that I can think of ( listed with disadvantages of each)
Static function 'hasLoop' in Linkedlist.java ? ( this is weird, because if
I want to do hasLoop for existing instance, I would call it
LinkedList.mergeSort(instance) rather than instance.mergeSort() )
Non-static function 'hasLoop' in Linkedlist.java? ( this would be weird
because some functions like sort belong to collections )
Subclass an Linkedlist.java and add new function 'hasLoop' ? ( this would
be weird because if I need to add another function like say
findIntersection, I would need to create another subclass )
Somehow use Collections and add a static method 'hasLoop(List)', and add
additional interfaces into LinkedList.java to make it somehow possible ? (
it would be ugly as Node is private class with internal implementation,
and ptr.next cannot be performed by collections. It would need some
setters to modify state like setNext() etc.)