This MitPY comes from frequent commenter, John Friend:

*Dear Colleagues,*

*I gave a CAS-FREE question to my Specialist students whose first part was to solve (exactly) the equation *. *I solved it two different ways and got two different answers that are equivalent. I’ve attached my calculations.*

*I checked my answers using Mathematica, which lead to my question: Mathematica gives a third different but equivalent answer **(scroll down to real solutions). How has Mathematica got this answer?*

*It may be that Mathematica ‘used’ my Method 2, got my tan answer and then for some arcane reason ‘manipulated’ this answer into the one it finally gives. If so, I can ascribe the answer to a Mathematica quirk. But it may be that Mathematica is using a method unclear to me that leads to its answer. If so, I’m curious.*

*Any thoughts are appreciated.*