The difference between lengths of the radii is
(1.875-1.5)/2 = 0.1875
From the line, which is tangent to both circles:
The perpendicular distance from the line to the center of the smaller disk is the radius, or 0.75 inches.
The perpendicular distance from the line to the center of the larger disk is the radius, or 0.9375 inches.
We have a triangle:
We know the hypotenuse length (sum of the two radii) and we know then length of the opposite side (0.9375 - 0.75 = 0.1875 )
That is HALF of the total angle.
You will need to double the above to get the answer sought.