jmc

Define $$A=\frac{1}{1^2}+\frac{1}{5^2}-\frac{1}{7^2}-\frac{1}{11^2}+\frac{1}{13^2}+\frac{1}{17^2}-\cdots ,$$which omits all terms of the form $\frac{1}{n^2}$ where $n$ is an odd multiple of 3, and $$B=\frac{1}{3^2}-\frac{1}{9^2}+\frac{1}{15^2}-\frac{1}{21^2}+\frac{1}{27^2}-\frac{1}{33^2}+\cdots ,$$which includes only terms of the form $\frac{1}{n^2}$ where $n$ is an odd multiple of 3.

Determine $\frac{A}{B}.$