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.
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There is none because it is not true.
If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)
near zero
It is the reciprocal of the sine ratio.