I have a Mathematica program that outputs a piecewise function, and some parts of the expression are not being recognised as specific numbers when using `FullSimplify`. For example, in the output there is

```
ArcCos[3/5] + 2 ArcSec[Sqrt[5]]

```

which is actually equal to $\pi$, and there is also

```
ArcCos[3/5] - 2 ArcCos[2/Sqrt[5]]

```

which is actually equal to $0$. 

I was wondering if there was a way to have Mathematica recognise these sort of outputs in their more simplified form. I know that I can use numerical approximation, but was wondering if it was possible to do so while keeping the output in exact/closed form.