The value of $4\left(\sin ^4 30^{\circ}+\cos ^4 30^{\circ}\right)-3\left(\sin ^2 45^{\circ}-2 \cos ^2 45^{\circ}\right)$ is:

4

4 ( sin4 30º + cos4 30º ) - 3 ( sin² 45º - 2 cos²45º )

= 4 ( \(\frac{1}{16}\) + \(\frac{9}{16}\) ) - 3 ( \(\frac{1}{2}\) - 2 ×\(\frac{1}{2}\) )

= ( \(\frac{5}{2}\) ) - 3 ( \(\frac{1}{2}\) - 1 )

= \(\frac{8}{2}\) 

= 4