1. Your use of "*/1" is unnecessary. Unless I'm mistaken, all you need is the asterisk.
2. /etc/crontab is not root's crontab. The root user has a user-based crontab just like any other user. The /etc/crontab file and the files in /etc/cron.d are system-wide crontab files that are not associated with a specific user--they are generic "system" crontabs. They do not require use of the crontab command to install or modify.
So, appending a line to /etc/crontab, such as:
* * * * * root /tmp/myscript.sh
should work to run /tmp/myscript.sh as root once every minute.
Note, you will not be able to see the job listed under root or any other user's crontab by using "crontab -l"
If you do not believe the script is running, then check that your script uses absolute paths to programs and/or have the script write information to a log file to verify it is working.
You can read more by using man 5 crontab
-- the comments in the example crontab files explain that /etc/crontab is a "system" crontab file.