I dyed my Wulff TT from white to olive 2 years ago with RIT and it still looks as good as it did the day I bought it.
I boiled about 1 gallon of water, disolved the dye, added cold water to cool it down (you don't need it too hot, just a little hotter than what comes out of your faucet). Place the line loosely coiled in the dye bath until you get the shade you want, rinse with cold water.
It doesn't take long so don't leave it sitting.
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Rich