Integral $\int^{\pi/2}_{0} (\int^{\pi/2}_{0}f(1-{\sin\theta}{\cos\phi})\sin\theta d\theta ) d\phi= {\pi/2}\int^1_0f(x)dx$ [closed]

I need to prove the following relation: $\int^{\pi/2}_{0} \left( \int^{\pi/2}_{0}f(1-{\sin\theta}{\cos\phi})\sin\theta \,\, d\theta \right) d\phi= {\pi/2}\int^1_0f(x)\,\,dx$.

My guess is that this problem needs a suitable transformation of variables, so that the inner integral becomes independent of $\phi$.