# Regarding properties of Farey sequences related to lattice points.

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.