Sum of Squares of Two Standard Normals

Let $X_1, X_2 \sim \text{iid } N(0,1)$. Define $R = X_1^2 + X_2^2$.

(a) Switching to polar coordinates $(X_1, X_2) = (r\cos\theta, r\sin\theta)$, derive the joint density of $(R, \Theta)$ where $R = X_1^2 + X_2^2$ and $\Theta = \arctan(X_2/X_1)$.

(b) Marginalize over $\Theta$ to find the PDF of $R$ and identify its distribution.