lets first do it by a simple and short method...

by energy method...

lets work in frame of reference of sphere..

let P be the point where it makes an angle @ with the verticle...

forces acting on particle : pseudo force(=ma); weight(=mg) and normal reaction(=N) 

now, K.E at P = W_{pseudo force} + W_mg + W_N

1/2mv² = maRsin@ + mgR(1-Rcos@) + 0

solve to get v = [2R(asin@ + g -gcos@)]^1/2