The value of (sin² 30°. cos² 45°) + (5 tan² 30°) + \(\frac{3}{2}\)sin² 90° - 3cos² 90°:

3\(\frac{7}{24}\)

(sin² 30° . cos² 45°) + (5tan² 30°) + \(\frac{3}{2}\)sin² 90° - 3cos² 90°

= (\(\frac{1}{4}\) . \(\frac{1}{2}\)) + 5(\(\frac{1}{\sqrt {3 }}\))² + \(\frac{3}{2}\)(1)² - 3(0)

= \(\frac{1}{8}\) + \(\frac{5}{3}\) + \(\frac{3}{2}\)

= \(\frac{3 + 40 + 36}{24}\)

= \(\frac{79}{24}\)

= 3\(\frac{7}{24}\)