The oxidation number of Co in `[Co(en)_(3)]_(2)(SO_(4))_(3)` is
`+2`
`+1`
`+3`
`+6` .

Explanation

To determine the oxidation number of cobalt (Co) in the complex \([Co(en)_{3}](SO_{4})_{3}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the components of the complex**:
- The complex consists of cobalt (Co) coordinated with three ethylene diamine (en) ligands and is associated with three sulfate (SO₄) ions.

2. **Assign oxidation numbers**:
- Ethylene diamine (en) is a neutral ligand, which means it has an oxidation number of 0.
- The sulfate ion (SO₄) has an oxidation number of -2.

3. **Set up the equation**:
- Let the oxidation number of cobalt (Co) be \(X\).
- The coordination sphere consists of one cobalt and three ethylene diamine ligands, so the contribution from the ligands is \(3 \times 0 = 0\).
- The sulfate ions contribute \(-2\) for each ion, and since there are three sulfate ions, the total contribution is \(3 \times (-2) = -6\).

4. **Write the equation based on the charge balance**:
- The overall charge of the complex ion \([Co(en)_{3}]^{2+}\) must balance with the three sulfate ions, which have a total charge of \(-6\).
- Therefore, we can set up the equation:
\[ X + 0 - 6 = 0 \]
- This simplifies to:
\[ X - 6 = 0 \]

5. **Solve for \(X\)**:
- Rearranging the equation gives:
\[ X = +6 \]

6. **Determine the overall charge of the complex**:
- The complex ion \([Co(en)_{3}]^{2+}\) indicates that the oxidation state of cobalt is indeed \(+3\) when considering the overall charge of the complex.

### Final Answer:
The oxidation number of Co in \([Co(en)_{3}](SO_{4})_{3}\) is **+3**.