Is this avoidable?
If I can't avoid it can I solve it?
You cannot avoid this from happening, but you can avoid it from impacting you. The way the hardware works will not change, so inevitably you will shade some fragments more than once. Up to some point, this does not matter.
Smaller triangles generally give a "better look", but with diminishing returns. At some point, even smaller triangles do not give any benefit any more, but theamount of doubly-shaded fragments figuratively explodes.
The solution is to draw everything at its proper level of detail, and for the artist this means to either generate a model that contains discrete levels of detail, or something that will gracefully downgrade with an on-the-fly LOD algorithm. Ideally, all triangles as seen on the screen are approximately the same size.
Your main character's or an enemy's model might very well have 25,000 triangles for the head only when you look straight into his eyes. These 25,000 triangles will cover 80-90% of the screen, so that is perfectly OK.
On the other hand, the same model (head plus body) viewed at a virtual distance of 50 meters will cover an area of the screen coparable to your thumbnail, so it probably shouldn't have more than a few dozen or at most a hundred triangles. If a thumbnail-sized area on the monitor corresponds to 25,000 triangles, you're shading every fragment a thousand times and you gain no visual quality at all (in fact, it may very well cause nasty aliasing artefacts). If half of your screen consists of thumb-sized areas of thousands of triangles, you're in serious trouble.