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  1. This will require new frameworks for global cooperation in areas of investment, research and technology.
  2. This will require new frameworks for global cooperation in the areas of investment, research and technology.
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(First, "this" is vague; even with context, the reader may not know whether "this" refers to a specific noun in an earlier sentence or a condition described in an earlier sentence, paragraph, or section.)

The sentences have slightly different meanings. Since "areas of investment, research and technology" doesn't include the definite article "the", it could be interpreted to mean various facets within the fields of investment, research, and technology. Perhaps it refers to investment into emerging markets, corporate research, and military technology, for example. This meaning could be emphasized by adding a few clarifying words:

This [expansion/objective/modification] will require new frameworks for global cooperation in [certain] areas [within the fields] of investment, research and technology.

In contrast, the definite article "the" in "the areas of investment, research and technology" simply refers exactly to those stated general fields, all of which will require new frameworks for global cooperation.

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The second sounds much more natural to me.

I cannot give you a specific rule for this, but the following general observations may be useful. It seems to me that when 'in areas of' is followed by a single category you do not need to use the definite article, e,g,:

In areas of extreme poverty you will often find...

I will be in areas of the state where there has been drought.

Be careful if you are touring in areas of conflict.

If 'in areas of' is followed by more than one categories, then the definite article is required, e.g.:

He is an expert in the areas of health, psychology and administration.

They conduct business in the areas of waste management, recycling and treatment of industrial waste.

You can also use the expression 'in the area of' when it is only followed by a single category, e.g.:

He is an expert in the area of health.

I would like to work in the area of Public Relations.

The phrase 'in the area of' is also used to indicate an approximate location or amount, e.g.:

Your salary will be in the area of $120,000 annually.

I have pain the in the area of my kidneys.

All people in the area of Sacramento are encouraged to participate.

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