Multiply both sides of the equation in Part I by (cos theta)^2.
This will result in (cos theta)^2 + (sin theta)^2 = 1.
(Recall that (sec theta)*(cos theta) = 1.)
I believe the answer is cos^2 theta. Sec^2 theta on the right side of the equation is the inverse of Cos^2 theta, so multiplying the two together will get you 1. Cos^2 theta * Tan^2 theta = Sin^2 theta, and Cos^2 theta * 1 = Cos^2 theta. This all leads to the third and last step in the picture above.
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