Send this trap to an SNMP manager — replace <manager> with the IP or hostname of your monitoring server (SNMPv2c):

snmptrap -v2c -c public <manager> '' T3610-MIB::trapEmailErrAuth
snmptrap -v2c -c public <manager> '' 1.3.6.1.4.1.22626.0.3

Listen for incoming traps on the manager host (-f keeps it in the foreground, -Lo prints to stdout — useful for testing):

snmptrapd -f -Lo -c /dev/null authCommunity log public

Example snmptrapd log entry:

zoo11-linux.zoo [UDP: [192.168.30.111]:63360->[192.168.30.10]:162]:
  DISMAN-EVENT-MIB::sysUpTimeInstance = Timeticks: (513604480) 59 days, 10:40:44.80
  SNMPv2-MIB::snmpTrapOID.0 = OID: T3610-MIB::trapEmailErrAuth

SNMPv3 example:

snmptrap -v3 -l authPriv -u snmpv3user -a SHA -A "AuthPass1" -x AES -X "PrivPass1" <manager> '' T3610-MIB::trapEmailErrAuth