Is there any relationship between the "theo" in "theoretical" and that in "theology"?
Solution 1:
No, the prefix theo- means "God" from which theology. Theory derived from "theoria" meaning "contemplation sight":
Theo-
- word-forming element meaning "god, gods, God,*" from comb. form of Greek theos "god," from PIE root *dhes-, root of words applied to various religious concepts, such as Latin feriae "holidays," festus "festive," fanum "te
Theology
- mid-14c., "the science of religion, study of God and his relationship to humanity," from Old French theologie "philosophical study of Christian doctrine; Scripture" (14c.), from Latin theologia, from Greek theologia "an account of the gods," from theologos "one discoursing on the gods," from theos "god" (see theo-) + -logos "treating of" (see -logy). Meaning "a particular system of theology" is from 1660s.
Theory
- 1590s, "conception, mental scheme," from Late Latin theoria (Jerome), from Greek theoria "contemplation, speculation; a looking at, viewing; a sight, show, spectacle, things looked at," from theorein "to consider, speculate, look at," from theoros "spectator," from thea "a view" (see theater) + horan "to see," possibly from PIE root *wer- (4) "to perceive" (see ward (n.)).
Etymonline
From The Westminster PresbyterianA Ministry of the Presbytery of the United States:
An ancient, though erroneous, etymology of the word theoria viewed it as a derivative of theos. Although this etymology has been shown to be untenable, the word has both a background and a usage permeated with religious significance.
A theoros was one who consulted an oracle or was present as a spectator at a religious feast. Theoria in the sense of philosophical contemplation or vision was cultivated by the Pythagoreans as a religious way of life. Plato uses the term to refer to metaphysical vision of the eternal forms in which mathematical order is fused with religious aspiration. Aristotle represents theoria both as the goal of human life and as that in which God's own blessedness consists.