SQL Server transaction log backups: test whether tail log follows last known log backup

SQL Server transaction log backups: test whether tail log follows last
known log backup

We are using SQL Server with full recovery mode. Given a full backup and a
series of log backups, we would like to be able to check whether the log
chain is complete from the last full backup to the current tail log.
(Without actually restoring these backups; the purpose here is to test the
consistency of the backups.)
I already know how to do this for the existing backups: using RESTORE
HEADERONLY I get the FirstLSN and LastLSN of every file, which can be
compared for consecutive files, in order to determine whether they are
compatible.
However, I don't know how to check whether the tail log follows the last
log backup.
If I had the FirstLSN of the tail log, I could compare it to the LastLSN
of the last log backup. But how can I obtain the FirstLSN of the tail log?
I need a solution that works from SQL Server 2005 upwards (ideally using
t-sql). So far, I have searched Google to no avail. Btw. I first posted
this on stackoverflow; but migrated it here since it was flagged off-topic
there.