The sum of all values of x in [0, 2$$\pi$$], for which sin x + sin 2x + sin 3x + sin 4x = 0, is equal to :

The number of solutions of sin⁷x + cos⁷x = 1, x$$\in$$ [0, 4$$\pi$$] is equal to

The number of solutions of the equation x + 2tanx = $${\pi \over 2}$$ in the interval [0, 2$$\pi$$] is :

The number of roots of the equation, (81)^sin2x + (81)^cos2x = 30 in the interval [ 0, $$\pi$$ ] is equal to :