Is this the correct reflection coefficient?

For the structure in attached picture, should the Gama (reflection coefficient)=(Zin2-Zin1)/(Zin2+Zin1)?

I was wondering if it is Gama=(Zo2-Zo1)/(Zo2+Zo1), but I highly doubt it is the correct one to use.

It is the input impedances looking into each side that really matter. But I cannot think of a better justification.

Any one can help some insight?

Viewn from the connection point, only Zin1 and Zin2 are real. The line impedances are internal details of the connected ports that must not necessarily be known.

Thank you FvM for comments. Using characteristic impedance for calculation does not make sense.

Just wondering why most textbook are not giving a more general case of using zin1 and zin2? What is up with that?

I was thinking of this a little more: when the reflected wave travels down the line, at least at the beginning moment, it is seeing the input impedance as the characteristic impedance of the transmission line.

The consideration would be right for a pulse respectively wide band matching problem. In the general case, reflection coefficients are frequency dependent and measured with continuous signals, so there's no "beginning moment". On the other side, you'll only achieve a frequency independent reflection coefficient if the "arbitrary load" equals the line impedance, or in other words Zin = Z0.