Write the sum of geometrical isomers in
`[Pt(H_(2)N-CH(CN_(3))-COoverset(Θ)O)_(2)]` complex and stereoisomers of `[Pt(gly)_(3)]^(o+)` complex .

Explanation

To solve the question, we need to determine the sum of geometrical isomers for the complex \([Pt(H_2N-CH(CN_3)-CO^{\Theta}O)_2]\) and the stereoisomers for the complex \([Pt(gly)_3]^{o+}\).

### Step-by-Step Solution

**Step 1: Analyze the first complex \([Pt(H_2N-CH(CN_3)-CO^{\Theta}O)_2]\)**

1. **Identify the coordination number and geometry**:
- The platinum complex has a coordination number of 4, which typically leads to a square planar geometry.

2. **Identify the ligands**:
- The ligands are \(H_2N\) (amine), \(CN_3\) (cyano), and \(CO^{\Theta}O\) (carbonyl). The complex has two identical ligands.

3. **Determine possible geometrical isomers**:
- In a square planar complex, the two types of arrangements are cis and trans.
- **Cis isomer**: Both \(H_2N\) and \(CO^{\Theta}O\) are adjacent to each other.
- **Trans isomer**: The ligands \(H_2N\) and \(CO^{\Theta}O\) are opposite each other.

4. **Optical activity**:
- The ligand \(H_2N-CH(CN_3)-CO^{\Theta}O\) is unsymmetrical, making the cis isomer optically active.
- The trans isomer is not optically active due to symmetry.

5. **Count the geometrical isomers**:
- We have 2 isomers for the cis configuration (due to optical activity) and 2 for the trans configuration.
- Total geometrical isomers = 2 (cis) + 2 (trans) = 4.

**Step 2: Analyze the second complex \([Pt(gly)_3]^{o+}\)**

1. **Identify the coordination number and geometry**:
- The coordination number is 6, which indicates an octahedral geometry.

2. **Identify the ligands**:
- Glycinate (gly) can coordinate through both nitrogen and oxygen, making it a bidentate ligand.

3. **Determine possible stereoisomers**:
- In an octahedral complex with three bidentate ligands, we can have different arrangements.
- The arrangement can be in alternating positions (N, O, N, O, N, O) or interchanged positions (N, O, O, N, N).

4. **Count the stereoisomers**:
- Each arrangement can exist in two forms (D and L configurations).
- Therefore, for each arrangement, we have 2 stereoisomers.
- Total stereoisomers = 2 (for one arrangement) + 2 (for the second arrangement) = 4.

**Step 3: Calculate the total isomers**

- Total geometrical isomers from the first complex = 4.
- Total stereoisomers from the second complex = 4.
- Therefore, the sum of geometrical isomers and stereoisomers = 4 + 4 = 8.

### Final Answer
The total number of isomers (geometrical + stereoisomers) is **8**.