To count the number of opening parentheses in the given string, we can go through the string character by character and count each occurrence of the character `'('`. 

Let's analyze the string:

```
"()((()(()((()()((()))()((()(()(((()((()())))()(())()))())()(())((()()((()(()((()()((()))()((()(()(((()((()())))()(())()))())()(())(((()((()())))()(())()))())()(()))()(((()((()((()()((()))()((()(()(((()((()())))()((()((()(()((()()((()))()((()(()(((()((()())))()(())()))())()(())((()))()(((()((()((()()((()))()((()(()(((()((()())))()(())()))())()(())(((()((()())))()(())()))())()(()))()))())()(())(((()((()())))()(())()))())()(()"
```

Counting the opening parentheses `(` in this string:

1. Each opening parenthesis `(` will be counted, while closing parentheses `)` will be ignored.
2. We can use a programming language or manually count.

Let's proceed with the counting:

### Manual Count

Counting the opening parentheses `(` in the full string:

After going through the string, we find that there are **128** opening parentheses.

Therefore, the answer is:

**128** opening parentheses.
