I understand you guy's point but you only look at one way of solving, which is (for example by plotting) comparing the LHS to the RHS in a strict sense. I perfectly understand that if you calculate the LHS "as is" you won't arrive to the RHS simply because arctan() is bound to [-Pi/2, Pi/2], I perfectly agree with that.
But if you do it in the other way i.e. isolating the atan() term you end up with a solution that doesn't matter how much n*Pi terms you have inside the LHS/RHS.
-Pi/2 - atan(25x) - n*Pi = -2*Pi/3
atan(25*x) = Pi*(1/6 - n)
x = tan(Pi(1/6 - n))/25 = (1/sqrt(3))/25
On that matter this is why I prefer the "robustness" of the solve() under Maxima, which doesn't strictly evaluate LHS - RHS == 0
In a sense it's useful that it can be "smart" enough to see there's a solution to x when considering tan() is periodic.
If the solve() function strictly has to respect LHS = RHS, I think it would not hurt to have another function which can violate RHS=LHS, because it's useful when dealing with periodic functions and their opposite. My problem mostly arises from evalutating the phase of steady state s-domain systems for example, in which you can have equations (solved numerically) of the kind -A*y - B - atan(C*y) - atan(D*y) ... = 0 (because those equations can be easily extracted by inspection, but won't be necessarily perfectly formatted, the formatting being an extra step)
It somewhat becomes painful to check the bounds are respected (so that a solution exists) and would be (in this case) more useful to be able to "just get it" like I can with Maxima. I understand the math sense, but it would still be useful to be able to do that in Maple.