Do you need the exact angle in degrees/radians or does an approximated -1 to 1 value system work? If so, you can do a dotproduct(up, view). It should give you the values 1 when looking up, 0 when forward and -1 for down. I assume the vectors are already normalized.
Otherwise I am pretty certain that if you just drag a line from a vector and type angle you should get some helper functions to get it in radians or degrees.