Write out the initial angle of divergence equation on paper with the pencil, noting that the "0" stands for the angle of divergence:
0=(2/π)*(λ/2 w0)
Plug in the radius of the beam to the "w0" portion of the equation, and plug in the wavelength of the laser to the "λ" portion:
0=(2/π)*(40/2*4)
Solve the equation with the calculator by dividing π, or 3.14159265, by 2, to give you 1.57 when rounded to the nearest hundredth. Multiply 1.57 by the final number in the parentheses; in this case, 40 divided by 2 is 20, and multiplied by 4, the final number is 80, so multiply 1.57 by 80.
Write the angle of divergence of the beam down on the paper with the pencil; in this case, 80 times 1.57 is 125.6, so the angle of divergence of the beam is 125.6.