Torah U'Madda

First, an assumption (and if we disagree, then this post is moot): Not every aspect of Mada will enhance the quality of Talmud Torah. So, although the Gra reportedly felt that it is imperative to learn math and he knew Euclid's work well, we have no source that he felt it was important to be versed in the oeuvre of Tiepolo.
Now, how will one's Mada studies enhance the quality of his Torah study? One of three ways:

1. By accident. (I can't begin to tell you how happy I was to understand a Rashi that referenced niello-work just a few days after I happened to read about it in the dormitory bathroom's Britannica.)
2. By design - one already knows that learning this will help one's learning, as others have already trodden this path. Learning the Ayil Meshulash is a good example, or listening to the Kuzari about music, or to one's teachers who identify any specific field or topic as beneficial.
3. By hit-or-miss. One studies as much Mada of whatever variety one can find or is interested in, and hopes that some of it will be useful. (This is different from the first method, because there one's intention was not even to study - some Mada that one picked up happened to be useful. Here, one tries to make that accident repeat itself using the brute-force method - cram as much Mada into one's head as possible, so that there is a larger likelihood that some of it will be useful in enhancing the quality of one's Torah knowledge.)

The problem with the first method is that there is much Torah that will not be understood fully because of the fluky nature of this method. The problem with the third method is that it's extremely inefficient and still leaves the possibility of being unsuccessful - what if one's particular interests don't coincide with any Torah he learns?
If I had to stereotype, I would say that the most right wing of Torah Jews favor the first method (or possibly even less than that). The most left wing probably tend to favor the third method (or less than that - where Mada becomes an end in itself).