Help me setup this u substitution ? (just a simple trig function)

So I have been working on this integral but I am stuck because I am not very good with u sub.

So I am down to: tan^2 ( Y * pi/6) dy
Since there is no general form for tan^2 i thought i should put it in terms of sec^2 since we have a rule for that:
sec^2 (Y * pi/6) - 1 dy

But now I am not sure what to do, I am not good with differentials or integrating or substitution. To simply reverse the chain rule I am pretty sure I would need a pi / 6 multiplying that sec^2 function right?

you've done very well and you're almost there. just note that tan(x) differentiates to sec^2(x)

so you can integrate straight from that final line.


so the final answer is:
6/pi tan(y*pi/6) - y