Step 1: \textbf Calculate the number of years between the two dates.
\[
2040 - 2023 = 17 \text{ years}
\]
Thus, the period from \(15^{\text{th}}\) August 2023 to \(15^{\text{th}}\) August 2040 spans \(17\) years.
Step 2: \textbf Count the leap years in this interval.
The leap years occurring before \(15^{\text{th}}\) August 2040 are:
\[
2024,\; 2028,\; 2032,\; 2036,\; 2040
\]
Hence,
\[
\text{Number of leap years} = 5
\]
Step 3: \textbf Calculate the total odd days.
Every year contributes one odd day, and each leap year contributes one additional odd day.
\[
\text{Total Odd Days}
=
17 + 5
=
22
\]
Now,
\[
22 \mod 7 = 1
\]
Therefore, there is a net advancement of \(1\) day.
Step 4: \textbf Determine the required day.
Given:
\[
15^{\text{th}} \text{ August, 2023} = \text{Tuesday}
\]
Adding \(1\) day:
\[
\text{Tuesday} + 1 = \text{Wednesday}
\]
Hence, Independence Day in the year \(2040\) will be celebrated on Wednesday.