For this problem we just need to apply Breadth first search and return the last used node from the queue.
If you imagine the tree to be implemented not with nodes, but as an array (just like in the Heapsort), you will notice the deepest element is also the last element in the array.
Considering we have nodes and not a flat array, putting the nodes in a queue (with the Breadth first search) will build a queue just like the heapsort would do, with the deepest element being the last one.