Factor the trigonometric expression. \[ 25 \sec ^{4} w-60 \sec ^{2} w+36 \]

Step 1 ：Rewrite the given trigonometric expression as a quadratic equation in terms of sec^2(w). It can be written as (5sec^2(w) - a)^2 = b, where a and b are constants.

Step 2 ：Solve for a and b by comparing coefficients.

Step 3 ：The factored form of the given trigonometric expression is \((5 \sec ^{2} w-6)^{2}\)

Step 4 ：\(\boxed{(5 \sec ^{2} w-6)^{2}}\) is the final answer.