Is someone permitted to force another person to do an aveira (sin) by threat of death, [If the person doing the forcing does not actually intend to carry out his threat]? If not, why not? Since the person doing the aveira does not know that the person threatening him will not actually kill him, he isn't doing any Aveira, because he's considered a oness (acting unwillingly). Thus, the person forcing him is not causing him to do an aveira. So why should it be forbidden?
Regarding if it is a sin when being forced to do it, you may have a proof from this משנה ברורה.
The משנה ברורה סי' ש"ו ס"ק נ"ח answers a contradiction about being מחלל שבת to save someone being forced to do an עבירה. He says, if it's a one time עבירה we are not מחלל שבת, because חילול שבת is also an עבירה. However, if it's a lifetime of עבירות, we are מחלל שבת. Obviously, doing an עבירה even when forced is still an עבירה.
If it is an עבירה, it would be forbidden because of לפני עור.