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A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R$. The angle of projection, $\theta$, is then given by:
A
$\theta=\cos^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$
B
$\theta=\sin^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$
C
$\theta=\sin^{-1}\left(\frac{2gT^2}{\pi^2R}\right)^{1/2}$
D
$\theta=\cos^{-1}\left(\frac{gT^2}{\pi^2R}\right)^{1/2}$