A conical pendulum is formed when the bob moves in a horizontal circle.

And theta is < 90 for a conical pendulum; else the problem reduces to circular motion in a horizontal plane. 
That was implied.
My equation could involve cosine if theta represented the angle between
the vertical plane and the plane normal to the conical pendulum.
T = 2 pi sqrt (Lcos theta / g )

Can you please demonstrate how you came to this result?
And just because a method gives a right answer, it does not mean it is right.

True. Let me try to demonstrate why I think I'm right.
Let's say that a pendulum swings side to side in a period of 3 seconds,
covering 30 cm.
Now, lets take that same pendulum and let it spin horizontally,
it would still cover 30 cm from side to side, but would also move along
another plane, unaltering the period....I'm sorry if that doesn't make sense.