You said you applied plumbers tape, but sight unseen I would bet you got the wrong tape.

Those cheap little blue&white rolls of PTFE(teflon) tape commonly found in all the hardware and home supply stores are single density Teflon tape.

Single density tape is only intended to by used on SAE & NPT threads up to 3/8".

You angle stop valve is no doubt a 1/2" NPT thread. For 1/2" and greater threads you should use the red triple density tape and even with the triple density tape it still requires three full layers to insure a seal.

You can find the red triple density tape in all Lowe's or HD stores in the section where they keep solders and soldering paste. You will find Yellow Rolls Double density tape (commonly labeled as "Gas Tape"), the tape is also yellow, and you will find RED rolls of Triple Density Tape. Although it is called Red, in reality the roll is red but the tape is a light pink color.

When applying the tape you begin on the end of the pipe and make one complete turn around the threads even with the end of the pipe then continue wrapping so that each wrap overlaps the successive wrap by 2/3 the width so that by the time you get to the solid part of the pipe at the end of the thread section you will have 3 full layers at any given point. The tape must be pulled to tension while wrapping to insure it gets down into the thread grooves.

Those cheap rolls of white single density tape are about $.99 a roll, expect to pay about $2.98 a roll for the triple density.

These were 3/8" threads, is there anything else that might cause this. Also, theoretically could you just wrap the threads three times to accomplish the same thing as one wrap with the triple density tape?

One more thing, is there any truth to the drip just to clog its self up and stop?

if it is a 3/8 nipple then the white tape is fine to use.

no, teh leak will not stop itself. if anything it will get worse. first try to tighten it a little more. if that does not work, then remove it and redo the tape. i bet you wrapped it the wrong way.

If you talking about the 3/8 tap on the discharge side of the angle stop that is a compression fitting. Compression fittings are precision ground fittings and you should never apply any dope or tape on compression fittings. Dope and tape is only to be used on NPT (National Pipe Taper) threads.