Simplifying atan?



How would one go about showing that atan((5*sqrt(2)+4)/(3*sqrt(2)+16))
is equal to atan((2*sqrt(2)+5)/(8*sqrt(2)+3))?

It's easy enough to show that the args of the atan's are the same, but
I want maxima to determine that the difference between the atan's is
0.  Note that these two atan's are part of two different expressions
that involve other atan's and logs and the two expressions are
supposed to be equal.  I can get the logs to go away via logcontract,
but not the atan's.

What am I missing?

Ray