The value of sin36°·sin72°·sin108°·sin144° is:

Supplements repeat the values: sin108° = sin72° and sin144° = sin36°, so the product is $(sin36°\cdot sin72°{)}^2$. Now 2·sin36°·sin72° = cos36° − cos108° = (√5 + 1)/4 + (√5 − 1)/4 = √5/2, so sin36°·sin72° = √5/4 and the square is 5/16 = 0.3125. Check: $0.58779\times 0.95106\times 0.95106\times 0.58779=0.3125$. Squaring only the surd in √5/4 gives √5/16, and forgetting that the last two factors repeat the first two gives 1/16.