1. Hint-lines
Perhaps more attention should be paid to the hint-lines that connect the point of the triangle with the place where it should be. And then you can pay less attention to the color of the shapes and their shape, which fill the triangles. Before I introduced hint-lines into the game, it was much harder to solve puzzles.

2. Symmetry of hint-lines
It is necessary to achieve the symmetry of the lines within the same circle. What I mean is visible on gif n.2. No matter how we turn it rotates the circle - the length of all lines remains the same. As soon as we see that some line is breaking beyond the others, it is necessary to pay attention to it. That is, if the length of all the lines is the same, it is immediately clear that you can rotate the circle so that all the points are in place.

3. Isolated circles
These are separate circles that have one intersection point with the rest of the puzzle. Isolated circles must be solved first of all - that is, those circles that are on the periphery of the figure and if all the points on it are in place - then you can forget about this circle and not use it - don't touch it - don't rotate. When an isolated, outer circle is assembled - no longer pay attention to it. From now on, the puzzle is simplified.

4. Splitting the puzzle into components, simpler parts
Break the puzzle into simpler components - into fragments consisting of only two circles and solve them first.

5. Intersection points between two circles
Circles can have 1 intersection point or 2 (with one, of course, easier). If the circles have one intersection point, then you have to keep two points in your head - where is the desired vertex of the triangle and where should it be moved (especially since the circles rotate all the time and the points change their position accordingly).
If there are two intersection points, then you have to keep in mind the change of four vertices at once. Stock up on patience and paper.
There is nothing shameful to sketch some puzzle states, mark some standard solutions, take screenshots at last.
So again briefly:
- Rotate each circle of the puzzle carefully, returning it to the same place (maybe you will see the symmetry of the lines)
- Simplify the puzzle by assembling it in parts
- The game does not encourage thoughtless rotation - this way it will not be solved - it will only become more incomprehensible and perplexed
- This is a game where thinking about each move and the presence of paper and pens for sketching and notes are welcome
Yes, this is just a theory, so a little later I will analyze all this with concrete examples, solving puzzles of the TRIZ game.