This is exactly how I got the answer first time in post#24

No . I had actually employed the strategy as suggested by you when I wrote the answer in post#24 . After getting the right answer , then I tried applying Star Delta approach .
Your approach is quite admirable !
Please help me understand one thing i.e how could the middle line drawn ( to exploit symmetry ) coincide with the resistor between T and M .
I am still unsure how we could remove resistor between T and M .
Please reflect a little more on this symmetry aspect .