Yes, it can.
If you plot theta and sin(theta) on the same graph, you will see where they intersect.
I do not know of an analytical expression for this point; I think only numerical results are possible.
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If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
Yes. (Theta in radians, and then approximately, not exactly.)
For such simplifications, it is usually convenient to convert any trigonometric function that is not sine or cosine, into sine or cosine. In this case, you have: sin theta / sec theta = sin theta / (1/cos theta) = sin theta cos theta.
sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)
near zero