Question 37
Determine all values of the real parameter $a$ for which the equation
$$
8^a \sin^2 x = 4 \cdot 2^{\cos^2 x}
$$
has exactly one solution in the interval $\left[-\frac{\pi}{6}, \frac{2\pi}{3}\right]$.
$$
8^a \sin^2 x = 4 \cdot 2^{\cos^2 x}
$$
has exactly one solution in the interval $\left[-\frac{\pi}{6}, \frac{2\pi}{3}\right]$.