8 sin π/4 cos 3/4 + cos² phi/6 - sin² 3/4 phi =

sin π/4 = 1/2 √2
cos 3/4 π = -1/2 √2
cos 1/6 π = 1/2 √3
sin 3/4 π = 1/2 √2

8 sin π/4 cos 3/4 + cos² phi/6 - sin² 3/4 phi =
8(1/2 √2)(-1/2 √2) + (1/2 √3)² - (1/2 √2)²
=8.(-2/4) + (3/4) - (2/4)
=-4+3/4-2/4
=-16+3-2 / 4
=-15/4