Estimate the angular diameter of your thumb, held at arm's length.

Well, this depends on the length of your outstretched arm from the joint of your shoulder to the joint of your thumb finger. Mine is 21 inches long. My thumb is 2.5 inches long. The angular diameter can be determined using the trigonometric functions. We can use the tangent function

tan θ = opposite side/adjacent side = thumb's length/shoulder-to-finger length

tan θ = 2.5 in/21 in

θ = 6.79°