Hello i have this question that i am struggling to answer regarding changing variables, i really dont know how to do it

A gun fires at random in the angular range −π/2 < θ < π/2 towards a wall a distance 'l' away. If 'y' is the coordinate along the wall,

show that

g(y)dy=(1/π) (1/(1 +(y/l)^{2})) (dy/l)

This is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L either side of the peak. Calculate the new normalisation constant, and find the standard deviation.