find argument and modulus of z=1+itan(theta)

Arg z=theta, and modulus(z)= sec (theta)

case1 0<theta<pi/2

case 2: pi/2<theta< pi

case 3: pi<theta<3pi/2

case 4: 3pi/2<theta<pi

here x=1 and y =tan theta so either the complex no lies in the first quadrant or the fouth quadrant so case 2 and 3 shld be invalid ,but in text there is an anwer for each case hw is that possible ,pls share ur ideas