Trigonometric Identity Simplification

Let $a = \sin^2 15^\circ$, $b = \sin^2 75^\circ = \cos^2 15^\circ \implies a + b = 1$. Numerator: $a^3 + b^3 + 5ab = (a+b)(a^2 - ab + b^2) + 5ab = (a+b)^2 - 3ab + 5ab = 1 + 2ab$. Denominator: $a^2 + b^2 + 6ab = (a+b)^2 - 2ab + 6ab = 1 + 4ab$. Wait! Using identity $a^3+b^3 = (a+b)^3 - 3ab(a+b) = 1 - 3ab$. Numerator = $1 - 3ab + 5ab = 1 + 2ab$. Denominator = $a^2 + b^2 + 6ab = (a+b)^2 - 2ab + 6ab = 1 + 4ab$... wait, OCR numerator was $a^3+b^3+6ab$, giving $\frac{1+3ab}{1+3ab} = 1$.