HELP.

sec = 1/cos      csc = 1/sin   so we need sin and cos for all of the objects

5pi/6    sin = 1/2        cos =   - sqrt3/2

5pi/4    sin = - sqrt2/2    cos = -srt2/2

11pi/6   sin = -1/2      cos  = sgrt3/2

so ....adding all of these inverses

2 - 2 /sqrt3    - 2/sqrt2   -  2/sqrt2   - 2 + 2/sqrt3   =  -   4 / sqrt 2   = - 4 sqrt 2/2   = - 2 sqrt 2