Mahamrityunjaya Mantra and the importance of its first word

ॐ त्र्यम्बकम् यजामहे सुगन्धिम् पुष्टिवर्धनम् ।

उर्वारुकमिव बन्धनान् मृत्योर्मुक्षीय मामृतात् ।।

aum tryambakaṃ yajāmahe sugandhiṃ puṣṭi-vardhanam

urvārukam iva bandhanān mṛtyor mukṣīya māmṛtāt

[Another poular versino is]

ॐ [ह्रौं ॐ जूं सः भूर्भुवः स्वः] त्र्यम्बकं यजामहे

सुगन्धिं पुष्टिवर्धनं |

उर्वारुकमिव बन्धनान् मृत्योर्मोक्षिय मामृतात् ||"
[बूर्बुवः स्वरों जूं सः ह्रौं ॐ]

Please read the details about it here Mahamrityunjaya_Mantra

This is all known but what I have noticed is the importance of the first word त्र्यम्बकं trayambakam. *Traya=3, Ambakam=eye; meaning the one who is 3 dimensional, or 3 eyed one or 3 eyed reality or the one who sees 3 dimensionally or sees everything. *amba=mother; so traya/trya=3(brahma vishnu maheswara the hindu trinity), the mother of 3, that means it also represents the same message of gayathri mantra where it worships the one true god. *Here trya/traya can also represent 'THE THREE' or 'THE Trinity' that is vrahma(a), vishnu(u), maheshwara(m) meaning aum and the amba=mother. so traymabakam=brahma vishnu maheswara and the amba(mother) *if you consider here traya symbolizing the 3 eyed then amba the mother, so tryambakam may well mean shiva and amba or shiva and shakti or shashakti.