Summation of trigonometry functions

Geometry Level 4

$\large\dfrac{\sin^2{0^{\circ}}+\sin^2{10^{\circ}}+\sin^2{20^{\circ}}+\sin^2{30^{\circ}}+\ldots+\sin^2{180^{\circ}}}{\cos^2{0^{\circ}}+\cos^2{10^{\circ}}+\cos^2{20^{\circ}}+\cos^2{30^{\circ}}+\ldots+\cos^2{180^{\circ}}}$

If the value of the above expression is $\large\dfrac{a}{b}$ where $a$ and $b$ are coprime positive integers. Find the value of $a^2+b^2$ .