MathNet 2008-part-05 — 164 problems (EN–VI) Question 107

Suppose that $a, b, c, d$ are real numbers satisfying $a \geq b \geq c \geq d \geq 0$, $a^{2} + d^{2} = 1$, $b^{2} + c^{2} = 1$, and $a c + b d = 1/3$. Find the value of $a b - c d$.