Learn English – You tried vs You did try

I'll switch the "goal" to something a little more specific...

If you say "I am trying to eat more fresh fruit", the normal implication is you're making that effort right now. It doesn't say much about how long you've been trying, or how successfully. So most likely there's also the implied meaning that you haven't reached your goal of eating sufficient fresh fruit yet.

If you say "I try to eat more fresh fruit", the normal implication is that by habit, for some significant amount of time, you've been eating more fresh fruit than you would have done if you hadn't bothered to make any effort in that direction. So must likely the implied meaning is you do in fact eat enough fresh fruit, but you're aware (and are reminding someone else) that it requires some effort for you to achieve this.

OP's "I try to calculate the minimum angle..." would therefore be an unlikely thing to say, because you wouldn't normally be in the habit of doing this. That's not to say it's an invalid construction - it's perfectly grammatical. But you'd probably only use it in some contrived "narrative" context chronologically and sequentially describing each thing that you do, as you do it.

If I understood the sequence of events correctly, your letter should look roughly like this:

I'm writing to report that I've already sorted out the problem. Thank you for the suggested solution. I had tried this solution before receiving your letter though.

Using the Past Perfect is okay here: you're mentioning an event in the past: trying out the solution, and then a subsequent event: receiving their letter.

You may use did try to put more stress on the fact that you tried this solution:

I'm writing to report that I've already sorted out the problem. Thank you for the suggested solution. I did try this solution before receiving your letter though.

But did try would look better in a letter telling that you still haven't sorted out the problem, as a way to reassure them that you've indeed tried it.

If you use "I have tried that" it will look ambiguous: the construction will leave them guessing when exactly did you try the solution: before you received their letter with the suggestion or after.