3458 is to convert from radians to arc-minutes
180/pi (deg/radian) * 60 minutes/degree = 3,437.7467707849398
3438 is the common rounded used number.
23.6mmx15.8mm sensor use smaller for circle to fit is 15.8 mm
divide by two for the angle is 7.9 mm
Tan-1, Arctan(7.9/1300) = 0.3481778°
multiply by 2 is now 0.6963555°
alternatively working in arc-mins ( the calculator, avoids trig functions based on sin Ø ~= Ø (rads) when angles are under 1°, (cosØ~=1) this is the assumption the calculator works with to get approx close calc)
sensor height x convert radians to arcmins (180/pi*60) / focal length gives
1300 mm x ~3438 / 1300mm =
41.78184536800157 arc mins ( calc rounded to
41.78492307692308 arc min (close enough))
41.7818 / 60 = 0.69636408946669°
~same as working with trig
you are missing a factor of approx 2x somewhere.
It is probably in the barlow now is acting as a lens ( telescope is lens #1, barlow #2, and so your distance from this second lens becomes a magnifying effect, like in a view camera where you move the camera lens by extending the bellows and can macro/magnify what the lens does at infinity.
here is the math:
F = focal length of objective or primary
f = focal length of Barlow 
J = joint focal length (effective focal length)
d = separation of Barlow and original focal plane (objective focal plane)
x = separation of barlow and new focal plane (eyepiece focal plane)
M = amplification of Barlow
J = (F×f)/(f-d) ...(1) (combined lens formula) ***********
M = J/F ...(2) (by definition)
The separation of the Barlow and the new focal plane can be calculated from M and f:
x = f×(M-1) ...(3)
...from which we get :
M = 1 + (x/f)
math ( I am assuming you amount adapter is going to cause a 2x magnification BEYOND the 2x of the barlow itself)
- Based on Separation of Eyepiece Focal Plane and Barlow
Let us take a 75mm focal length x2 (nominal) Barlow used at its designed amplification. (f = 75mm, M = 2)
M = 1 + (x/f)
δx = f(M - 1) = 75(2 - 1) mm = 75mm
This relationship (the separation of Barlow and the new focal plane is equal to the focal length of the Barlow) holds for any x2 Barlow.
Let us now use the old trick of increasing Barlow amplification by inserting an extension tube to the camera, the t-mount, (working here much like a star diagonal between the eyepiece and Barlow), is between the camera and the barlow.
Assume that the extensions adds 150mm to the optical path.
('guessed' from 75*3)
M = 1 + (x/f) = 1 + (75 + 150)/75 = 4.0
i.e. a nominal x2 Barlow has become an x4 Barlow.
- Based on Separation of Objective Focal Plane and Barlow.
Let's take a 130mm f/10 objective (F = 1300mm) with
a 75mm focal length Barlow (f)
placed 56.25mm inside focus (d).
('guess' 56.25 from 75/4 = 18.75, 75-18.75 = 56.25)
Substituting in equation (1):
J = (F×f)/(f-d)
= (1300 × 75)/(75-56.25) mm
Substituting in equation (2):
M = J/F
Hence we have an amplification factor of ×4.
Substituting in equation (3):
x = f×(M-1)
= 75 × (4 - 1) mm
I hope that explains how the t-mount tube has changed your math
your barlow is effectively 225mm
by this 56.25mm (2") extension.