First, let's simplify the expression inside the parentheses:

1 3/4 + (10 1/3 - 4 5/6)
= 1 3/4 + (10 2/6 - 4 5/6)
= 1 3/4 + (10 2/6 - 4 5/6)
= 1 3/4 + 5 9/6
= 1 3/4 + 5 3/2
= 1 3/4 + 3 1/2
= 4 2/4 + 3 2/4
= 7 4/4
= 8

Now, we have:

(2 3/16 + 8 : 2 1/5) : 6 7/8

Next, let's calculate the division inside the brackets:

2 3/16 + 8 = 16/16 + 3/16 = 19/16 = 1 3/16

1 3/16 ÷ 2 1/5 = 19/16 ÷ 11/5 = 19/16 * 5/11 = 95/176 ≈ 0.5398

Now we have:

(1 3/16 + 0.5398) : 6 7/8

1 3/16 + 0.5398 = 19/16 + 5398/10000 = 19000/16000 + 5398/10000 = 7298/5000 = 1.4596

1.4596 : 6 7/8 = 1.4596 ÷ 55/8 = 1.4596 * 8/55 = 0.2127

Therefore, the final answer is approximately 0.2127.