Get output of trig function as a multiple of pi?

General Usage
11

I think the way is to overload print:

julia> struct PiF
         x
       end

julia> function Base.show(io::IO, x::PiF) 
         y = rationalize(x.x/π)
         print("($(y.num)/$(y.den))π")
       end

julia> function Base.print(stdout::IO,x::AbstractVector{PiF})
         print("[")
         for i in firstindex(x):lastindex(x)-1
           print("$(x[i]), ")
         end
         print(" $(x[end])]")
       end

julia> println(v)
[(2/3)π, (1/3)π, (1/4)π ]

julia> print(v)
[(2/3)π, (1/3)π, (1/4)π ]