Newbie wants advice on venting closet

Its been about 9 years since I last growing experience that I still feel like it was my 1st time. Well I got a closet thats about 4 by 3 feet and 8 feet high with a 400W hps in there. Summer is slowly coming and its already in the 85-90f in there. So Ive been thinking about someway to vent the place. And shouldnt I be the luckiest grower alive, I see on the ceiling that the dryer exhaust in passing through that same closet. So im guessing I could Y this flexible tube that goes out of the dryer. When I move out I could just un "Y" it. Is there a tight way of sealing these tubes nicely together? Any home made stuff that would be cheap is fine but I could also put in a few bucks and buy it depends.. all ideas welcome

i have a closet similar to yours only mine is slightly bigger than 2ft. by 4 ft. by 8 ft tall. I have a 400 watt mh vegging all my plants in there and i have a 1000 w hps in a 4 x 4 x 7 ft high sun hut for flowering. i would recommend you to veg with a mh because you get better compact vegitative growth where as a hps causes plants in veg phase to stretch.
I have a legnth of 4 inch ducting taped close to the underside of the lamp that sucks off heat with a 130 cfm blower. and i open my closet about 10 inches and taped a 6 ft piece of mylar to the opening leaving over a 1 ft gap at the top and a large gap at the bottom where i can put a fan to get more circulation. My temps in there never get higher than 85 degrees.

1st complication, I was observing the outside wall of the building where are located the exhaust system exit. And Im 99% sure that the tube passing through my closet is the neighbors dryer exhaust from the next floor. Is there a device you can buy that ll let the neighbor dryer flow go outside and not in my grow room? And at the same time it would let the air im pumping out of the coset go outside and no into my neighbors dryer..