To solve this expression, we will first simplify the terms inside the parentheses and then divide by 1 2/21.

Step 1: Simplify the terms inside the parentheses (11,1÷3 - 2 1/6):
11,1÷3 = 11 + 1/3 = 33/3 + 1/3 = 34/3

2 1/6 = 2 + 1/6 = 12/6 + 1/6 = 13/6

Therefore, the expression inside the parentheses becomes:
34/3 - 13/6

Step 2: Find a common denominator for 34/3 and 13/6, which is 6:
34/3 = 68/6
13/6 = 13/6

Now the expression inside the parentheses becomes:
68/6 - 13/6 = 55/6

Step 3: Divide by 1 2/21:
To divide by a mixed number, we can convert the mixed number into an improper fraction and then divide.
1 2/21 = 1 + 2/21 = 21/21 + 2/21 = 23/21

Now divide 55/6 by 23/21:
(55/6) / (23/21) = (55/6) (21/23) = (55 21) / (6 * 23) = 1155 / 138 = 35/4

Therefore, the final answer is 35/4.