Yes, theine is in the scrabble dictionary

...and is worth 9 points by itself.

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Theine Definition

noun

Caffeine when present in tea.

from the English-language Wiktionary

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Here are some other words you could make with the letters THEINE, you can also
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Top Words by points	Points
theine	9

2 letter words with THEINE	Points
en	2
eh	5
ne	2
it	2
in	2
te	2
ti	2
hi	5
he	5
et	2

3 letter words with THEINE	Points
the	6
ten	3
tee	3
tie	3
nth	6
tin	3
nit	3
nee	3
eth	6
hen	6
het	6
hie	6
hin	6
hit	6
net	3

4 letter words with THEINE	Points
hent	7
nite	4
hint	7
teen	4
tein	4
thee	7
then	7
thin	7
tine	4

5 letter words with THEINE	Points
thein	8
thine	8

6 letter words with THEINE	Points
theine	9

Found 37 words in 0.17687 seconds