If the equation cos⁴ $$\theta $$ + sin⁴ $$\theta $$ + $$\lambda $$ = 0 has real solutions for $$\theta $$, then $$\lambda $$ lies in the interval :

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 :

The value of
$${\cos ^3}\left( {{\pi \over 8}} \right)$$$${\cos}\left( {{3\pi \over 8}} \right)$$+$${\sin ^3}\left( {{\pi \over 8}} \right)$$$${\sin}\left( {{3\pi \over 8}} \right)$$
is :

The equation y = sinx sin (x + 2) – sin² (x + 1) represents a straight line lying in :