2 1/5 liters of water and 1 1/3 liters of juice are used for a team breakfast.

To find the total amount of drink used for the breakfast, you need to add the amount of water and juice together.

First, let's convert the mixed numbers to improper fractions.

For the water: \[ 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} \]

For the juice: \[ 1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \]

Now we need to add \(\frac{11}{5}\) and \(\frac{4}{3}\). To do this, we need a common denominator. The least common multiple of 5 and 3 is 15.

Next, we convert each fraction:

For \(\frac{11}{5}\): \[ \frac{11}{5} = \frac{11 \times 3}{5 \times 3} = \frac{33}{15} \]

For \(\frac{4}{3}\): \[ \frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15} \]

Now we can add the two fractions: \[ \frac{33}{15} + \frac{20}{15} = \frac{33 + 20}{15} = \frac{53}{15} \]

To convert \(\frac{53}{15}\) back to a mixed number, we divide 53 by 15: \[ 53 \div 15 = 3 \quad \text{remainder} \quad 8 \] So, \[ \frac{53}{15} = 3 \frac{8}{15} \]

Thus, the total amount of drink used for the breakfast is: \[ \boxed{3 \frac{8}{15}} \text{ liters} \]