Let ABCD be a convex quadrilateral, with diagonals AC and BD. At each vertex the diagonal makes an angle with each of the two sides, creating eight corner angles.
<imgclass="img-responsive center-block"alt="convex quadrilateral ABCD, with diagonals AC and BD"src="https://cdn.freecodecamp.org/curriculum/project-euler/integer-angled-quadrilaterals.gif"style="background-color: white; padding: 10px;">
For example, at vertex A, the two angles are CAD, CAB.
We call such a quadrilateral for which all eight corner angles have integer values when measured in degrees an "integer angled quadrilateral". An example of an integer angled quadrilateral is a square, where all eight corner angles are 45°. Another example is given by DAC = 20°, BAC = 60°, ABD = 50°, CBD = 30°, BCA = 40°, DCA = 30°, CDB = 80°, ADB = 50°.
What is the total number of non-similar integer angled quadrilaterals?
**Note:** In your calculations you may assume that a calculated angle is integral if it is within a tolerance of ${10}^{-9}$ of an integer value.