Determine the exact value of the following trigonometric expression without the help of the calculator.

tan^-1 [tan(-π/3)]

Determine the exact value of the following trigonometric expression without the help of the calculator.

tan^-1 (tan 3π/4)

Transform the following expression into an algebraic expression. Use a right triangle in writing the algebraic expression. Assume that the inverse trigonometric function is defined for its argument and assume that x > 0.

sin (tan⁻¹ 4x)

Find the solution of the equation on the interval [0, 4] using a calculator. Round the answer to four decimal places.

$\left(\arctan x\right)^3-3x+5=0$

Determine the angle measure $\theta$ without using a calculator. Express the answer in degrees.

$\theta=\arcsin\left(7\right)$