This circuit doesn’t have any independent source, so to find out thvenin’s equivalent resistance across 1 & 2 connect a 1 volt voltage source across the terminals and find the current (I) through voltage source. The circuit can be redrawn as,

Applying KCL at node A

                ---------- (1)

Apply KCL at node B

                -----------(2)

Using (1)

                -----------(3)

Applying KVL in the loop

                -----------(4)

Also

                ----------(5)

From 3, 4 & 5 -