How to solve this recursive equation ? The answer is also given. can anyone give an detailed explanation how to solve it ??????

q(t) = 4 − (2/q(t-1)), with t>=2 -----------(1)

Answer is :

q(t) = (2 - sqrt(2)) +[ (2.sqrt(2) / (1- (3-2.sqrt(2))^t] ------------------(2)

Now, equation (1) is not a simple homogeneous linear second order equation which we normally use to solve recurrence problems. The product term q(t).q(t-1) makes the polynomial equation of higher order. Can anyone kindly explain me in detail the solution procedure of the equation ???? It will be very helpful if you write your detailed solution procedure in a piece of paper and send me that as a scanned copy or PDF.

See attachment.