In this method, a node at the specified position in the circular doubly linked list is deleted. For example - if the given list is 10->20->30 and the 2nd node is deleted, the list becomes 10->20.

First, create two nodes temp and nodeToDelete to traverse through the list and track the node to delete respectively. After that count the number of elements in the list to check whether the specified position is valid or not (It must lie in the range of [1, n], where n is number of elements in the list). If the specified valid position is 1 and head is the only element in the list, then make the head as null. If the specified valid position is 1 and list contains more than one elements, then make next of head as new head and adjust links accordingly. If the specified valid position is greater than 1 then traverse to the node previous to the given position and delete the given node and adjust links accordingly. The function pop_at is created for this purpose. It is a 5-step process.

```void pop_at(int position) {

//1. create two nodes - temp and nodeToDelete
//   to traverse and track the node to delete
Node nodeToDelete = head;
Node temp = head;
int NoOfElements = 0;

//2. Find the number of elements in the list
if(temp != null) {
NoOfElements++;
temp = temp.next;
}
while(temp != head) {
NoOfElements++;
temp = temp.next;
}

//3. check if the specified position is valid
if(position < 1 || position > NoOfElements) {
System.out.print("\nInvalid position.");
} else if (position == 1) {

//4. if the position is 1 and head is the only element
//   in the list, then make it null, else make next
//   of head as new head and adjust links accordingly
if(head.next == head) {
head = null;
} else {
while(temp.next != head)
temp = temp.next;
head = head.next;
temp.next = head;
head.prev = temp;
nodeToDelete = null;
}
} else {

//5. Else, traverse to the node previous to
//   the given position and delete the given
//   node and adjust links accordingly
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp.next;
nodeToDelete = temp.next;
temp.next = temp.next.next;
temp.next.prev = temp;
nodeToDelete = null;
}
}
```

The below is a complete program that uses above discussed concept to delete a node at a given position in the circular doubly linked list.

```//node structure
class Node {
int data;
Node next;
Node prev;
};

class LinkedList {
Node head;

LinkedList(){
head = null;
}

//Add new element at the end of the list
void push_back(int newElement) {
Node newNode = new Node();
newNode.data = newElement;
newNode.next = null;
newNode.next = null;
if(head == null) {
head = newNode;
newNode.next = head;
newNode.prev = head;
} else {
Node temp = new Node();
temp = head;
while(temp.next != head)
temp = temp.next;
temp.next = newNode;
newNode.next = head;
newNode.prev = temp;
head.prev = newNode;
}
}

//Delete an element at the given position
void pop_at(int position) {
Node nodeToDelete = head;
Node temp = head;
int NoOfElements = 0;

if(temp != null) {
NoOfElements++;
temp = temp.next;
}
while(temp != head) {
NoOfElements++;
temp = temp.next;
}

if(position < 1 || position > NoOfElements) {
System.out.print("\nInvalid position.");
} else if (position == 1) {
if(head.next == head) {
head = null;
} else {
while(temp.next != head)
temp = temp.next;
head = head.next;
temp.next = head;
head.prev = temp;
nodeToDelete = null;
}
} else {
temp = head;
for(int i = 1; i < position-1; i++)
temp = temp.next;
nodeToDelete = temp.next;
temp.next = temp.next.next;
temp.next.prev = temp;
nodeToDelete = null;
}
}

//display the content of the list
void PrintList() {
Node temp = new Node();
temp = this.head;
if(temp != null) {
System.out.print("\nThe list contains: ");
while(true) {
System.out.print(temp.data + " ");
temp = temp.next;
if(temp == this.head)
break;
}
} else {
System.out.print("\nThe list is empty.");
}
}
};

// test the code
public class Implementation {
public static void main(String[] args) {
LinkedList MyList = new LinkedList();

//Add three elements at the end of the list.
MyList.push_back(10);
MyList.push_back(20);
MyList.push_back(30);
MyList.PrintList();

//Delete an element at position 2
MyList.pop_at(2);
MyList.PrintList();

//Delete an element at position 1
MyList.pop_at(1);
MyList.PrintList();
}
}
```

The above code will give the following output:

```The list contains: 10 20 30
The list contains: 10 30
The list contains: 30
```