What is the domain of y=

Tan = sin / cos      we cannot have cos = 0   (denominator cannot = 0)

      cos = 0 at  odd multiples of pi/2      1/2 theta cannot equal on odd  multiple of pi/2

So  all theta not equal to odd numbers of pi     ( pi  3 pi     5 pi etc )

tan  A    will be undefned at   pi/2  +  n * pi

So    let  A  =    θ/2

So      θ /2  =  pi /2  +  n* pi        multiply through by 2

So      θ  =   pi  + n*2pi

So.....it will  be defined at all real numbers except    pi  +  2pi * n

So.... "d"  is correct...