To solve this problem, we need to find a common denominator for all the fractions. The least common denominator (LCD) for 3, 6, 10, 21, 28, 36, and 45 is 2520.

Now, we can rewrite each fraction with the LCD as the denominator:

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

Now, we can add all the fractions together:

(840/2520) + (420/2520) + (252/2520) + (120/2520) + (90/2520) + (70/2520) + (56/2520)

To add fractions, we need to have a common denominator. Since all the fractions already have the same denominator, we can simply add the numerators:

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

So, the sum of the fractions is 1848/2520.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 168:

1848/2520 = (1848/168) / (2520/168) = 11/15

Therefore, the sum of the fractions is 11/15.