@Kitonum 

Shall look for more examples...

(x1+0.7e-1*sin(30*x2)^2)^2+(x2+0.7e-1*sin(30*x1)^2)^2-1=0;

http://radikale.ru/data/upload/c2184/0fccf/c7cd7bb962.gif

(It is moving perpendicular and tangent to each point.)

Theta has a period of (2n+-1)* Pi, and x has a period of (2n+-1)* Pi

Theta has a period of (2n+-1)* Pi, and x has a period of (2n+-1)* Pi

restart;

 f := Z^6-3*Z^4+3*Z^2+Z-1;

for i to 6 do op(i, [evalf(solve(f))]) end do;

restart;

 f := Z^6-3*Z^4+3*Z^2+Z-1;

for i to 6 do op(i, [evalf(solve(f))]) end do;

With Maple?