What are angular sizes of thin and thick disks in our Galaxy? What are diapasons of galactic coordinates for thin and thick disks of our Galaxy?
The sun is usually taken as the center of the galactic coordinate systems. Our solar system is well within the thin disk of our galaxy (population I stars). So taking the headline question literally, we see the thin disk as well as the surrounding thick disk in almost every direction, meaning any galactic latitude and longitude.

The radius interval, where we find mostly stars of the thin or thick disk, varies with angles. Along the galactic plane the radius interval is across the galaxy (up to about 30 kilo parsecs, varying a bit with direction, because we are not in the center of the galaxy) for the thin disk, containing the sun as origin; perpendicular to the galactic plane it's about 1 kilo parsec to both directions for the thin disk, followed by a respective radius interval from 1 to 3 kilo parsecs for the thick disk, if I follow the Wikipedia articles referenced in the question.

The region dominated by the thick disk is the farther away from us the closer we look along the galactic plane.

There are certainly no sharp boundaries between the star populations. Actually the thick disk penetrates the thin disk, but it's much sparser populated.

The Gaia project may give a much more detailed answer about the distribution of stars within our galaxy in the next 5 to 10 years.