SEE THE NOTES IN THE ATTACHED PHOTO.
The codes prohibit the use of sanitary Tee's on a horizontal line. You must use a Wye fitting and you can then use a 1/8 bend (sanitary 45deg) to either turn at right angles or parallel to the pipes.
If you are under the International Residential Code the 2" shower line may run a maximum of 8' measured on the top of the pipe from the junction into the 3" main drain to the shower Trap. If you are under the Uniform Plumbing Code the length is limited to 5'. If the length of run exceeds these limits you would need to install an auxillary vent within those limits.
A vent line may not run horizontally until it it 6" above the flood level rim of the highest fixture served by the line.
The vent on the water closet line is not necessary and in fact a water closet will flush much better if the nearest vent is at least 3' away. (Vents are required to prevent the water in the traps from being syphoned out, however a water closet actually works on a syphon principal so having a vent too close will retard the rate of flush. In order to insure a water closet will not be left with a dry trap the fill valve has a trap primer line to refill the trap after the flush.)
You can install a 2" Wye and 1/8bend and run a horizontal line to the lavatory. Turn the line upwards through the wall behind the lavatory and install a Sanitary TEE (A Wye is prohibited here) and run a short waste arm out to the lavatory. Continue the 2" riser upwards until it is 6" above the flood level rim of the sink, then you can turn it horizontal and connect it to the existing 2" vent to the roof. The 3" under the floor would then be vented through the lavatory riser and the tub line is venting off the 3", provinding of course the length of the line from the 3" to the shower drain is within the above stated limits.
