What is the probability of two randomly chosen integers being coprime?

Bonus(d4): How does the result relate fo the density

of square-free numbers?

(In reply to

re: computer approximation (vs researched solution) by Charlie)

Interesting that the indicated solution, pi^2/6, is the inverse of the infinite sum 1/n^2 - the Basel problem, first proved by the incomparable master, Leonhard Euler.

Is there any deep significance in this?

Who knows?

In Euler's absence, any ideas, dear Perplexi?