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8 sin(π/4) cos(3π/4) + cos²(π/6) - sin²(3π/4)
= 8 sin(180/4) cos(540/4) + cos²(180/6) - sin²(540/4)
= 8 sin(45) cos(135) + cos²(30) - sin²(135)
= 8 √2/2 (-√2√2) + (√3/2)² - (√2/2)²
= 8 √2/2 (-√2√2) + 3/4 - 1/2
= 8 (-1/2) + 3/4 - 1/2
= -4 + 3/4 - 1/2
= -13/4 - 1/2
= -11/4