Even if you’re right, and the diaeresis/umlaut does change the pronunciation, how can you have any confidence that it will change the pronunciation to the one you want. Consider that you are trying to indicate a pronunciation that would be contraindicated in German orthography, which is the most likely language that an English speaker might know the symbol from.
There are two sounds indicated by ü in standard German. One is [y], which is a rounded * (“long”). The other is [Y], which is a rounded * (“short”).
I think that last character should actually be *.
ETA: Hey! The board changed it; that was supposed to be capitalized. I guess it’s trying to parse it weirdly because the brackets initially look like a tag or something…
As with all other vowels, the quality of the vowel will impact the sound that is made when pronouncing it. A “short” vowel, like a short vowel sound in English, is somewhat less intense than the long vowel sound.
But what exactly is a “long” or “short” vowel, anyway? Do phoneticists use such terms?
No, they don’t generally. That’s why I used quotation marks.
That’s right, the ü in *München *is not like the one in zurück, but neither one of them is supposed to sound remotely like ‘u’ in ‘put’. I find that ‘ee’ approximates ‘ü’ much better (but it is still only an approximation).
ETA: Only now do I see that the second I in square brackets is supposed to be capitalized!
As Indistinguishable noted the “I” gets jiggered by the board software.