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.

Notice that the odd legs are not on the horizontal line.