smc

There are either $$65+200=265$$ or $$66+200=266$$ days between the first two dates depending upon whether or not year $N+1$ is a leap year (since the February 29th of the leap year would come between the 300th day of year $N$ and 200th day of year $N+1$). Since $7$ divides into $266$ but not $265$, for both days to be a Tuesday, year $N$ must be a leap year. Hence, year $N-1$ is not a leap year, and so since there are $$265+300=565$$ days between the date in years $N,N-1$, this leaves a remainder of $5$ upon division by $7$. Since we are subtracting days, we count 5 days before Tuesday, which gives us $\boxed{\text{Thursday}}$