For followers of Islam to understand the concept of the Biblical Trinity, this can only be accomplished through the teachings found in their very own book of faith.
Since the goal of islam is to instruct Muslims that the Holy Bible is corrupt – no Biblical verse, or analogy will mean anything at all to them.
They will simply reject it.
Period.
All Muslims revere and trust their Koran. Thus, whatever is stated therein is the way that it must be.
To get through to them, you will need to use Koranic verses which demonstrate the concept of the Biblical Trinity.
One such Koranic ayah (which, ironically Muslims are trained to use all the time for their position) actually plainly states that the Trinity is not “three”, but instead, it is “one”, and then proceeds to list out Father, Son, and Spirit…
يأهل الكتب لا تغلوا في دينكم ولا تقولوا على الله
إلا الحق إنما المسيح عيسى ابن مريم رسول الله
وكلمته ألقيها إلى مريم وروح منه فءامنوا بالله
ورسله ولا تقولوا ثلثة انتهوا خيرا لكم إنما الله
إله وحد سبحنه أن يكون له ولد له ما في
السموت وما في الأرض وكفى بالله وكيلا
Ya ahla alkitabi la taghloo fee deenikum wala taqooloo AAala Allahi illa alhaqqa innama almaseehu AAeesa ibnu maryama rasoolu Allahi wakalimatuhu alqaha ila maryama waroohun minhu faaminoo biAllahi warusulihi wala taqooloo thalathatun intahoo khayran lakum innama Allahu ilahun wahidun subhanahu an yakoona lahu waladun lahu ma fee alssamawati wama fee al-ardi wakafa biAllahi wakeelan
4.171 You The Book's family, certainly do not go beyond the limits in your faith, and they do not say on “allah” except The Truth (is) only the Messiah Jesus, Mary's son, “allah’s” messenger, and his Word, cast forth to her, Mary, and Spirit from him; so believe on account of “allah”, and His messengers, and they do not say: "Three." Refrain (it is) agreeable certainly your only “allah” one god glory be to him, that He has certainly been his Son, truly His what is in the heavens and what is in the earth and He sufficed on account of “allah”, a witness.
Observe that this ayah is directed at ‘The Book’s family’ (ahla alkitabi) – which refers to the followers of the Holy Bible; i.e. Christians.
For the Muslim, it then gives instruction as to what the correct interpretation of the Holy Bible needs to be regarding (among numerous things), the concept of the Trinity.
In this classic Islamic one-hit-wonder we are told not to refer to the one “allah” as “Three”, as even his messengers do not say “Three” - because he is not the result of counted things (thalathatun)….and yet, in the very ayah itself it lists-out directly, Father, Son, & Spirit.
This is a classic Koranic example in which the authors display their understanding of the Biblical concept of the Holy Trinity, and give the example of what it is not by the usage of the word “Three”…and what it is, by the example of “one”.