cos 4 $\theta$ + sin 4 $\theta$ + $\lambda$ = 0 $\Rightarrow$ 1 – 2sin 2 $\theta$ cos 2 $\theta$ = -$\lambda$ $\Rightarrow$ 1 - $\frac{1}{2} \times 4$sin 2 $\theta$ cos 2 $\theta$ = -$\lambda$ $\Rightarrow$ 1 - $\frac{\sin^{2} 2\theta }{2}$ = -$\lambda$ $\Rightarrow$2($\lambda$ + 1) = sin 2 2$\theta$ 0 $\le$ 2 ($\lambda$ + 1) $\le$ 1 0 $\le$ ($\lambda$ + 1) $\le$ $\frac{1}{2}$ -1 $\le$ $\lambda$ $\le$ -$\frac{1}{2}$