To add these fractions together, we need to find a common denominator. In this case, the least common denominator is 2520.

1/3 = 840/2520
1/6 = 420/2520
1/10 = 252/2520
1/21 = 120/2520
1/28 = 90/2520
1/36 = 70/2520
1/45 = 56/2520

Adding them together:

840/2520 + 420/2520 + 252/2520 + 120/2520 + 90/2520 + 70/2520 + 56/2520 = 1848/2520

Therefore, 1/3 + 1/6 + 1/10 + 1/21 + 1/28 + 1/36 + 1/45 = 1848/2520 = 77/105.