Here is a brief MATLAB script I use to calculate a Beta Angle of about 8.80982 degrees for a spacecraft in a circular Mars orbit, compared to Thermal Desktop's calculated Beta Angle value of about 9.00216 with the same inputs:
L_s = 15; % longitude of sun (right ascension of sun)
orbInc_deg = 10; % relative to planet equator
orbRAAN_deg = 30; % from planet vernal equinox direction
equatorInc_deg = 25.19; % axis of rotation tilt relative to the ecliptic plane (inclination of equator relative to ecliptic plane)
decSun_deg = asind(sind(equatorInc_deg)*sind(L_s)); % solar declination relative to planet equator
BetaAngle_deg = asind((cosd(decSun_deg)*sind(orbInc_deg)*sind(orbRAAN_deg - L_s)) + (sind(decSun_deg)*cosd(orbInc_deg)))
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