Can someone do a calculation on a TI Inspire CAS?

[grsbanks]

That's pretty accurate.

For values of x around \(\pi\), \(sin(x) \approx \pi-x\)

The value of \(\pi\) is closer to 3.14159265358979, and \(3.14159265358979-3.141592654=-4.1021\times10^{-10}\) so I'd say this machine is right on the money.

The inaccuracy here isn't in the calculator, it's in the assumed value of \(\pi\).