Here we have the same ellipse but the figure has moved upward pi/4 = 45 degrees. We can shift the ellipse around the origin by continuing to increase what is subtracted from theta.
For instance:
We increased the rotation of the ellipse by subtracting pi/2, rather than pi/4, from theta.
Wheeeeeeeee!!!!!!
Look AT THAT Ellipse SPIN!
Basically, this equation is very much like the first one I explored. The only difference should be the location of the odd leg when n is odd.
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Notice that the odd legs are not on the horizontal line.