ORA-15055: unable to connect to ASM instance, ORA-01031: insufficient privileges

The today issue:
after installation GI and DB with role separation (grid and oracle) the DB cannot connect to ASM instance.

The DB process dedicated to connect to ASM is ASMB process. So, lets goo into the
$ORACLE_BASE/diag/rdbms/$DB/$SID/trace
and look $SID_asmb_$PID.trc files:

WARNING: failed to start ASMB (connection failed) state=0x1

In alert log you can see:
Thu Mar 21 13:18:29 2013
WARNING: ASM communication error: op 16 state 0x40 (1031)
ERROR: slave communication error with ASM
This means that grid user has not in asmadmin group. What you need is :
usermod -g oinstall -G dba,asmadmin  grid

But we still cannot connect to ASM, DB alert log still shows:

ORA-15055: unable to connect to ASM instance
ORA-01031: insufficient privileges

So, we need 2nd modification - add user oracle to asmdba group:
usermod -g oinstall -G dba,asmdba  oracle

Now all works and we see

NOTE: initiating MARK startup
Starting background process MARK
ORACLE_BASE from environment = /u01/app/oracle/
Thu Mar 21 14:08:07 2013
MARK started with pid=21, OS id=4206
NOTE: MARK has subscribed
Thu Mar 21 14:08:08 2013
ALTER DATABASE   MOUNT