Найдите значение выражения, задание прикреплю во вложении

Решите задачу:

$\frac{sin^4x+cos^4x+0,5sin^22x}{2cos2x+2sin^2x} =\\\\\star \; 1=1^2=(sin^2x+cos^2x)^2=sin^4x+ cos^4x+2\, sin^2x\, cos^2x=\\\\=sin^4x+cos^4x+2\cdot (\underbrace {sinx\cdot cosx}_{\frac{1}{2}sin2x})^2=sin^4x+cos^4x+2\cdot \frac{1}{4}sin^22x=\\\\=sin^4x+cos^4x+\frac{1}{2}sin^22x\; \; \star \\\\\star \; \; cos2x=cos^2x-sin^2x\; \; \star \\\\= \frac{1}{2(cos^2x-sin^2x)+2sin^2x}= \frac{1}{2cos^2x} = \frac{1}{2cos^2\frac{\pi}{3}} = \frac{1}{2\cdot (\frac{1}{2})^2}=\frac{1}{2\cdot \frac{1}{4}}=2$