To solve this expression, we follow the order of operations (PEMDAS).

First, let's simplify the first part of the expression:
5 4/45 - 4 1/6
Convert mixed numbers into improper fractions:
= (545 + 4)/45 - (46 + 1)/6
= (225 + 4)/45 - (24 + 1)/6
= 229/45 - 25/6
Find a common denominator:
= (2296 - 2545)/(45*6)
= (1374 - 1125)/270
= 249/270
Reduce the fraction:
= 83/90

Now, moving on to the next part of the expression:
(4 2/3 + 0.75) 3 9/13
Convert mixed numbers into improper fractions:
= (43 + 2)/3 + 0.75 (313 + 9)/13
= (12 + 2)/3 + 0.75 (39 + 9)/13
= 14/3 + 0.75 48/13
Find a common denominator:
= (1413 + 348)/39
= (182 + 144)/39
= 326/39

Now, moving on to the last part of the expression:
34 2/7 + 0.3 : 0.01/70 + 2/7
Convert mixed numbers into improper fractions:
= (347 + 2)/7 + 0.3 : 0.01/70 + 2/7
= (238 + 2)/7 + 0.3 : 0.000142857 + 2/7
= 240/7 + 0.3:0.000142857 + 2/7
= 240/7 + 0.3 : 142.857 + 2/7
Convert the division into multiplication:
= 240/7 + 0.3 70/0.01 + 2/7
= 240/7 + 0.3 7000 + 2/7
= 240/7 + 2100 + 2/7
Find a common denominator:
= (2407 + 2100*7 + 2)/7
= (1680 + 14700 + 2)/7
= 16382/7

Now, let's simplify the entire expression:
(83/90) : (326/39) (16382/7)
= (83/90) (39/326) (16382/7)
= (833916382) / (90326*7)
= 5131647 / 206940
= 66.978

Hence, the final result of the expression is 66.978.