understand that the inverse tangent function only yields values between -90 and +90 degrees, and angles that differ by 180 degrees have the same tangent value.

using a calculator in degree mode, note that

is very close to

.

since the angle you want is between 360 and 720, add successive multiples of 180 ...

-77+180 = 103 ... not large enough

-77 + 360 = 283 ... not there, yet

-77 + 540 = 463 ... ok, but there is another

-77 + 720 = 643

so, note you get two valid solutions in the desired range. 463 and 643 degrees.

take the tangent of both angles in your calculator to confirm.