Implement LinkedBinaryTree for this. This is a complicated thing implementing an interface which extends many other interfaces, and requires additional classes such as ArrayPositionIterator which implements PositionIterator.
You need not implement everything. Error conditions can be ignored. However, if you ommit an implementation, still have the method present, just return null or some other harmless value.
The object-oriented construction here is very complex, and I was thinking of just presenting a simplified version. However, it would be good practice in object-oriented design to walk through this now. In practice, I generally strike a different balance between generality (pure object-oriented design) and practicality (less levels of inheritance, less abstraction, more concrete data representations).