Determine point of intersection between two geographic rays We are currently looking for an equation to calculate the geographic point of intersection when given two geographic rays, where both thetas are angles based off true north (the bearing). Both points have different latitudes and longitudes. We are not very familiar with the intricacies of calculating points for geographic locations, so any help or information is greatly appreciated! 
Furthermore, I apologize for the quality of the image, I drew it quickly. Each theta should be numbered 1 & 2 respectfully. 

Thank you in advance!

Illustrating the comments by @JohnWaylandBales:

          


          

Great-circle arcs lie on planes through the sphere center.


So intersect the two planes, which determine a line through the sphere center,
which pierces the sphere at the arcs intersection point.
