${\sin ^2}2\theta \, + \,{\cos ^4}2\theta \, = \frac{3}{4}$

Let $\,{\cos ^2}2\theta \, =t $

$ \Rightarrow \,1\, – \,\,{\cos ^2}2\theta \, + \,{\cos ^4}2\theta \, = \frac{3}{4}$

$ \Rightarrow t = \frac{1}{2}\, \Rightarrow \,\,{\cos ^2}2\theta \, = \frac{1}{2}\,$

$ \Rightarrow 2\,{\cos ^2}2\theta  – 1 = 0\, \Rightarrow \,\cos 4\theta \, = 0$

$ \Rightarrow \,4\theta \, = (2n + 1)\frac{\pi }{2}$

$ \Rightarrow \,\theta \, = (2n + 1)\frac{\pi }{8} \Rightarrow \theta  = \frac{\pi }{8},\frac{{3\pi }}{8} \in \left[ {0,\frac{\pi }{2}} \right]$

Sum of values of $\theta $ is $\frac {\pi }{2}$