Math Problem Solver

The real solutions are: \[\begin{aligned}x &= \left\{\frac{\pi \left(1 + 4 n\right)}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.5707963\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(7 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.6651914\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(11 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.7595865\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{2 \pi n + \arctan{\left(\frac{\sqrt{10} - \sqrt{2}}{2 \sqrt{5 + \sqrt{5}}} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.31415927\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi + 2 \pi n + \arctan{\left(\frac{\sqrt{2} + \sqrt{10}}{2 \sqrt{5 - \sqrt{5}}} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.0840704\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi - \arctan{\left(\frac{\sqrt{10} - \sqrt{2}}{2 \sqrt{5 + \sqrt{5}}} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.8274334\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \arctan{\left(\frac{\sqrt{2} + \sqrt{10}}{2 \sqrt{5 - \sqrt{5}}} \right)} + 2 \pi + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.3407075\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]