Find the exact value of the expression.
\[
\tan \left(\sin ^{-1} \frac{4}{5}-\cos ^{-1}(-1)\right)
\]

Step 1 ：\(\sin^{-1}(4/5)\) returns the angle whose sine is 4/5. This angle is approximately 0.93 radians.

Step 2 ：\(\cos^{-1}(-1)\) returns the angle whose cosine is -1. This angle is \(\pi\) radians.

Step 3 ：Subtract the angle from the inverse cosine function from the angle from the inverse sine function: \(\sin^{-1}(4/5) - \cos^{-1}(-1) = 0.93 - \pi\).

Step 4 ：The tangent of the difference of two angles can be found using the formula: \(\tan(a - b) = \frac{\tan(a) - \tan(b)}{1 + \tan(a)\tan(b)}\). In this case, \(a = \sin^{-1}(4/5)\) and \(b = \cos^{-1}(-1)\).

Step 5 ：Since \(\tan(\cos^{-1}(-1)) = 0\) (as the tangent of \(\pi\) is 0), the expression simplifies to: \(\tan(\sin^{-1}(4/5) - \cos^{-1}(-1)) = \tan(\sin^{-1}(4/5))\).

Step 6 ：\(\sin^{-1}(4/5)\) is the angle whose sine is 4/5. This angle forms a right triangle with opposite side 4 and hypotenuse 5. The adjacent side can be found using the Pythagorean theorem: \(\sqrt{5^2 - 4^2} = 3\).

Step 7 ：The tangent of this angle is the ratio of the opposite side to the adjacent side: \(\tan(\sin^{-1}(4/5)) = \frac{4}{3}\).

Step 8 ：Therefore, the exact value of the given expression is \(\boxed{\frac{4}{3}}\).