If $x = \sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}{{\tan }^{2n}}\theta } $ and $y = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } $ for 0 < $\theta $ < ${\pi \over 4}$, then :

Question

If $x = \sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}{{\tan }^{2n}}\theta } $ and $y = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } $

for 0 < $\theta $ < ${\pi \over 4}$, then :

x(1 + y) = 1