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Strange Rectangle 2

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

Cube Roots

Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.

Golden Construction

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

Absurdity Again

Age 16 to 18 Challenge Level:
What is the value of the integers $a$ and $b$ where $$\sqrt{8 - 4\sqrt{3}} = \sqrt a - \sqrt b ?$$