I am self studying Apostol's Dirichlet series and Modular Functions in Number Theory and need help in this question. Question is – let $n \ge 1$ and $T_n$ denotes the set of lattice points $(x, y)$ in triangular region defined by inequalities $1\le x \le n$ and $1\le y \le n$ and $n+1 \le x+y \le 2n$. Also $T'_n$ denotes the set of lattice points $(x, y)$ such that $\gcd(x, y) =1$.

Then prove that $$\; \sum _ {(b, d)\in T'_n}{1\over bd} = 1.$$
Here last line means prove that summation of all $1/ bd$ such that $(b, d)$ belongs to $T'_n$ is equal to $1$. I am not able to do latex work properly.


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