Longitude of the Ecliptic I originally went to math.stackexchange.com and they suggested I try here as well. 

I'm trying to figure out how to calculate times of moonrise and moonset for a given position on the earth on a particular date. I'm using Vallado's Fundamentals of Astrodynamics and Applications because there is an example in the book that lays out a simplified process. I'm stuck at the point where I'm trying to calculate Longitude of the ecliptic for the Moon. The formula is below where T = -0.013634497.


  λEcliptic = 218.32° + 481,267.8813T + 6.29Sin(134.9 + 477,198.85T) - 1.27Sin(259.2 - 413,335.38T) + 0.66Sin(235.7 + 890,534.23T) + 0.21Sin(269.9 + 954,397.70T) - 0.19Sin(357.5 + 35,999.05T) - 0.11Sin(186.6 + 966,404.05T)


The expected answer is -0.8412457°. However, I'm unable to figure out how to get this answer. My calculations are below: 


  1) 218.32° + 481,267.8813T = -6343.525
  
  2) 6.29Sin(134.9 + 477,198.85T) = 5.963779
  
  3) -1.27Sin(259.2 - 413,335.38T) = -0.900843
  
  4) 0.66Sin(235.7 + 890,534.23T) = -0.292285
  
  5) 0.21Sin(269.9 + 954,397.70T) = -0.126871
  
  6) -0.19Sin(357.5 + 35,999.05T) = 0.138211
  
  7) -0.11Sin(186.6 + 966,404.05T) = 0.054722


Simply adding or subtracting gets me -6338.688731. How can I get the value -0.8412457° from this. My trigonometry is rusty and I'm not sure how to get the right answer. Any help would be greatly appreciated. Thanks.
There's a mistake in the book (see page 280 on google books): the values for $\lambda_{ecl}$ and $\phi_{ecl}$ should be swapped. Your result is correct:
$$
-6338.688^\circ\text{ mod } (360^\circ) = -218.688^\circ,
$$
which is the value that is erroneously listed under $\phi_{ecl}$.