Calculate the coordinates of Point P given three known reference points and the observed angles between them from Point P.
This is an old surveyor's technique, not used much any more these days.
If you want to see how it's done, use your browser's "view source" function.
NOTE: The results are indeterminate (that means "wildly inaccurate") if all four points lie on (or sufficiently close to) a circle or a straight line. (TBD: Implement a sanity check to detect this situation)
ALSO NOTE: This method is based on simple plane trigonometry and does not provide a geodetic solution (that is, it doesn't take into account the ellipsoidal shape of the Earth). However, for geocaching purposes, the results are "close enough" if all the points in question are within, say, 50 miles or so of each other.