Two-port network: find fundamental parameters
I think there's no magic approach to this: these kind of &quot;ladder&quot; circuits (that's a name I invented right now) are always a pain.
I would transform the triangle R2, L, C in a star using the Y-\$\Delta\$ transform (that's actually a \$\Delta\$-Y transform in your case), so that the circuit looks like this:



simulate this circuit &ndash; Schematic created using CircuitLab
Now of course you can compute the series R1, Z1 and R3, Z3 that leaves you with a T network that is probably already solved in literature.