To solve this equation, we need to simplify the expression on the right side first.

First, let's simplify the expression inside the parentheses:
8/11 - 8/7

To subtract fractions, we need a common denominator. The least common multiple of 11 and 7 is 77.

Rewriting the fractions with the common denominator:
(8/11)(7/7) - (8/7)(11/11)
= 56/77 - 88/77

Now, subtract the fractions:
56/77 - 88/77
= (56 - 88)/77
= -32/77

Now, let's substitute this value back into the original equation:
1/7 - [(-1/3) - (-32/77)]

To subtract fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Rewriting the fractions with the common denominator:
1/7 - [(-1/3)(7/7) - (-32/77)(3/3)]
= 1/7 - ( -7/21 - (-96/231) )

Now, simplify the expression inside the brackets:
1/7 - ( -7/21 + 96/231 )
= 1/7 - ( -7/21 + 32/77 )

To add fractions, we need a common denominator. The least common multiple of 21 and 77 is 1617.

Rewriting the fractions with the common denominator:
1/7 - ( -7/21 )(77/77) + ( 32/77 )(21/21 )
= 1/7 - ( -539/1617 ) + ( 672/1617 )

Now, subtract and add the fractions:
1/7 + 539/1617 + 672/1617
= (1 + 539 + 672)/1617
= 1212/1617

Finally, simplify the fraction:
1212/1617 = 4/7

Therefore, 1/7 - [(-1/3) - (8/11 - 8/7)] = 4/7.