Are these angles on the surface of a sphere? If they are then regular trigonometric laws do not apply and you will need a "correction factor" to take into account the nature of the geometry.
According to Clairaut the angle alpha 0 can be found by sin α0 = sin α cos β. I think that means sin alpha times cos B. The equation is supposed to be the law of sines applied to the sides NE and NP however I am not seeing how the law of sines applies yet. I took trigonometry in college but this is a topic I could use some help on understanding.
Thanks in advance...