You have answered your own question.
what year is tha Remington sportsman 58 serial 143766v
what is the market value of a remington 20 gauge semi-automatic sportsman 58 shotgun?
The value of a 20 gauge Remington Sportsman 58 would actually depend on a number of things. A couple of those things would be the age and condition.
Numrich gun parts. Look under Remington SPT 58.
By the serial number and markings on the barrel.
75-400 USD
according to blue book of gun values 271,000 approximate sportsman 58 were manufactured between 1956 and 1963
You will need a good gunsmith. The information you seek is not readily available in published material.
Don't know for sure which you mean... Sportsman 1930-1947 Sportsman 48 1948-1968 Sportsman 58 1956-1963
First of all you have the "sportsman 48", "sportsman 58" and the "sportsman". If it is a plain sportsman it's value depending on it's condition is from 150 to 200 dollars.
Take it to a professional
Take it to a gunsmith