Possible Cause

CMP sensor malfunction.
Connector or terminal malfunction.
Erratic signal from CKP sensor.
Open circuit between main relay terminal "D" and distributor terminal "1B". See Fig 1.
Open circuit between distributor terminal "1D" and PCM terminal "4F".
Open circuit between distributor terminal "1A" and body ground.
Short to ground between main relay terminal "D" and distributor terminal "1B".
Short to ground between distributor terminal "1D" and PCM terminal "4F".
PCM malfunction.

Fig 1: Identifying DTC P1345: CMP Sensor Circuit Malfunction, Circuit & Connector Terminals

Courtesy of MAZDA MOTORS CORP.