I plotted a simple function with:

```
   npi2 = {π/2, 3 π/2};
   npi3 = {π/3, 2 π/3, 4 π/3, 5 π/3};
   npi4 = {π/4, 3 π/4, 5 π/4, 7 π/4};
   Plot[Sin[x]^2 Cos[x], {x, 0, 2 π}, Frame -> True, 
   FrameTicks -> {{Automatic, npi3}, {npi4, npi2}}]

```

[![enter image description here](https://i.stack.imgur.com/DKOoh.png)](https://i.stack.imgur.com/DKOoh.png)

But the desired case is to show the roots (which should be automatically calculated) of the function with a special `Ticks` which be on the `x-axis` (not as `FrameTicks`) (exactly on an horizontal axis passed through the origin)