There are three parts:
Part I: August 1 day, 2003 to February 3 1 day, 2003.
Part II: 20 14 1 October to 2004 12 3 1 February.
Part III: 20 15 10/0/to August 2005 1.
Known situation: leap year 366 days, average year 365 days.
2004 ÷ 4 = 100 1 has no remainder, so 2004 is a leap year.
2003 and 2005 are normal years.
The first part plus the third part is exactly equal to an average year, which is 365 days.
So the number of days from August 2003 1 to August 2005 1 is 366+365 = 73 1 day.
There are 7 days in a week, so 73 1 ÷ 7 = 104...3 The remainder is 3.
So the third day before August 2005 1 is Friday. According to this calculation, August 1 is Monday.