Have I gone wrong with this?
Making y the subject:
Can you do that with arctan?
The problem is not the arctan but that "C". Just taking the reciprocal of both sides, .
Now, multiplying both numerator and denominator by 3, .
Of course, if "C" is some undetermined constant, so is 3C. You could write it as
but you should understand that "C" and "C' " are not the same number.
I gave you the explanation why it was wrong: does not imply . eg. 1/2 = 1/4 + 1/4 does not imply 2 = 4 + 4.
You are advised to review and/or take care with the basic algebra (the fact that you're working at the level of inverse trig functions means that the algebra I have explained is assumed knowledge).