Solve ∫ (from - 3 / 2 to pi / 2) of cos^2θdθ/sin^2θ+(frac{pi{R})^2}

$$\int _ { - 3 / 2 } ^ { \pi / 2 } \frac { \cos ^ { 2 } \theta d \theta } { \sin ^ { 2 } \theta + ( \frac { \pi } { R } ) ^ { 2 } }$$

Differentiate w.r.t. R

$$\frac{\mathrm{d}}{\mathrm{d}R}(\int _{-\frac{3}{2}}^{\frac{\pi }{2}}\frac{\left(R\cos(\theta )\right)^{2}}{\left(R\sin(\theta )\right)^{2}+\pi ^{2}}\mathrm{d}\theta )$$