would this also work?

Use [my database]

alter database [my database] set recovery simple

--Backup LOG with NO_LOG

Use [my database]

BACKUP LOG [my database] WITH NO_LOG

--Shrink log files

Use [my database]

DBCC SHRINKFILE (1)

DBCC SHRINKFILE (2)

--Change recovery mode back to FULL

Use [my database]

alter database [my database] set recovery FULL

-- FULL database backup when completed